Phy-Vec8
Transcript
00:00:00Hello, Assalamualaikum to everyone, let's see if the kids can hear me or not, can they see me or not.
00:00:20Hello Assalamualaikum
00:00:50As we were walking back and forth, we met each other again.
00:00:58Then tell me, how is life going on?
00:01:03Has there been any change in life?
00:01:07Or is life going on as it was?
00:01:11Tell me.
00:01:14Okay, so how is everyone's condition? I hope everyone is fine.
00:01:20The class that we are going to do today is a very interesting class.
00:01:28You will see that after doing the class, you are shouting.
00:01:32A very beautiful class.
00:01:34The concepts that we are going to discuss today are actually very beautiful.
00:01:39Very beautiful, okay?
00:01:42Okay, so let's start slowly.
00:01:48Is the sound low? No, the sound is absolutely fine. I just checked.
00:01:53The sound is very loud.
00:01:55The sound is so loud.
00:01:57If you take it near a glass, the glass will break.
00:02:01Did you understand?
00:02:03I hope the sound is clear.
00:02:06Everyone join quickly.
00:02:09We will discuss some very interesting concepts today.
00:02:16Is it okay?
00:02:18Okay.
00:02:20So Rab, you don't have to worry about these things.
00:02:23The way I am teaching today, come forward in the same way.
00:02:27The way each class is coming forward, follow it before each class.
00:02:33Understand it well.
00:02:35Because the vector study works as a foundation for each chapter in front of us.
00:02:41It takes a lot of time and effort to make a foundation for a building.
00:02:46Once the foundation is laid, it does not take much time to build the building.
00:02:51The same is true in the case of study.
00:02:53The foundation or the concepts that are there, it will take some time to build it.
00:02:59Then you will see that it will not take a lot of time.
00:03:03And Mashallah, you still have one and a half months left to start college.
00:03:07The way we are coming forward,
00:03:09If I give you an example of 25th,
00:03:12The exam will start on 25th.
00:03:16If I think very early, their exam will start in April next year.
00:03:21Now June,
00:03:23Our entire physics, first part, second part,
00:03:26There are four chapters left to study.
00:03:31And only four chapters are left to study.
00:03:36These five chapters will take about three to four months to study.
00:03:43Then October, November, December, January, February, March, April,
00:03:50It ends in October.
00:03:52That is, the entire syllabus ends six to seven months before the exam.
00:03:58If you have a full syllabus,
00:04:00Then maybe you won't get that much time.
00:04:03But the way we are coming forward, the flow is right.
00:04:06It is absolutely perfect.
00:04:08Leave this thing, this responsibility to us.
00:04:11Don't worry about this at all.
00:04:13Okay?
00:04:15Go and cover as much as you can.
00:04:17And then if you feel that I want to study more,
00:04:21Then come to our archive class.
00:04:23Then see the archive classes and move forward.
00:04:25Then when it comes to life class, do the life classes too.
00:04:27If you do the same thing two or three times,
00:04:30You will see that it will go well in your head.
00:04:32Can you understand?
00:04:34So don't worry about it at all.
00:04:36Those who are having trouble with the web app,
00:04:38You can come to Facebook.
00:04:40I am also reading comments on Facebook.
00:04:42Wait, I will enlarge the comment on Facebook.
00:04:44I will enlarge the comment on Facebook.
00:04:49Yes, it has become very big.
00:04:53Okay.
00:04:55Very beautiful.
00:04:57Okay.
00:04:59Give me some motivation today.
00:05:01Take this motivation.
00:05:03Do you want more?
00:05:05Take this motivation.
00:05:07Okay.
00:05:09Everyone is coming.
00:05:11Then we will start.
00:05:13First of all, we will discuss some rules of the vector world.
00:05:15We will discuss some rules of the vector world.
00:05:18And these are actually very obvious.
00:05:21For example, there is a formula called commutative law in English.
00:05:27See, what does this law actually mean?
00:05:29The law is like this.
00:05:31If I give an example with a number.
00:05:35If I give an example with a number.
00:05:37Suppose two numbers, 5 and 7.
00:05:40If we add these two,
00:05:42The result will come.
00:05:45If I add 7 and 5,
00:05:49Then our result will not come the same.
00:05:52The result will not come the same.
00:05:54What is this result?
00:05:55The result will not come the same.
00:05:57The result will definitely come the same.
00:05:59Is there any reason to add before and after?
00:06:01No.
00:06:03The same rule is followed in the case of vectors.
00:06:05The same rule is followed in the case of vectors.
00:06:08For example, suppose if two vectors are A and B.
00:06:13What will be the contribution of these two vectors?
00:06:17If you do not add B to A,
00:06:21If you add A to B,
00:06:25If you add A to B,
00:06:29Then the result will be the same.
00:06:32Then the result will be the same.
00:06:35For example,
00:06:38Suppose we have two vectors.
00:06:41This is our A vector.
00:06:44And this is our B vector.
00:06:47What is this vector?
00:06:49This is our A vector.
00:06:51And this is our B vector.
00:06:55Now, if I add B to A vector,
00:07:02What will be the contribution?
00:07:05To add B to A vector,
00:07:08We are thinking like this.
00:07:10The beginning and the end of one vector.
00:07:12The beginning and the end of the other vector.
00:07:14We can also add like this.
00:07:16When we add two vectors,
00:07:18When we add two vectors,
00:07:20When we draw an equation,
00:07:22The result will be the same.
00:07:23The result will be the same.
00:07:25Then,
00:07:27If we see the two vectors,
00:07:30What will be the contribution of these two vectors?
00:07:33The beginning and the end of the other vector.
00:07:35The beginning and the end of the other vector.
00:07:40Wait, I am not able to find the beginning and the end of the other vector.
00:07:43Oh, no.
00:07:45The beginning and the end of the other vector.
00:07:47Now, if you take this vector,
00:07:50And if you join the beginning and the end of this vector,
00:07:56Then the contribution will be equal.
00:08:00This is a contribution vector.
00:08:02And the vector I am drawing is the contribution of the green vector and the white vector.
00:08:08So, if you join the green and the white vector,
00:08:11The contribution will be equal.
00:08:13But, if I join the white and the green vector,
00:08:15The contribution will be equal.
00:08:20vector a b c. Arb joke kara je katha, br a joke kara kintu eki katha nirdesh kare.
00:08:28To bhaya, eto to amra dekhlam, amader duita vector jakhon hobe, takhon kar jonne. Jodi
00:08:34mone karen amarkase bar tinta vector ase, tahole ki hobe? Je mone karen amarkase tinta
00:08:39vector ase a b c. Mone karen ye vectorta aklam, ye vectorta hotse amader c vector.
00:08:47Takhole akhon, akhon amra ki, jodi aage a nahi, tarpare b nahi, ebon tarpare c nahi.
00:08:57Eta soman soman jodi amra, ektu orderta change kari, je aage b nilam, tarpare a vector nilam,
00:09:06tarpare c vector nilam. Ba jodi orderta onno rakam kari, c nilam, tarpare a nilam, tarpare
00:09:13b nilam. Sab khetre ki amader lobdhir maan ebon dik, aki rakam hobe? Sab khetre ki amader
00:09:20lobdhir maan ebon dik, aki rakam hobe? Dekhi chalo, amra etai ekto trial diye dekhi. Jaman,
00:09:27prothome dekho, a b c tinta lobdhir kamon habe? Ektar seser sate, arakta suru jog kollam,
00:09:34tarpare, eitar seser sate, eitar suru, e je, tahole lobdhir konta, lobdhir lalta diye
00:09:41prakash karchi, aadi theke ses, eta hotse lobdhita. Ekhon tumi jodi, eta to prothome
00:09:48a plus b plus c niso, jodi ebar tumi aage b nao, tarpare a nao, tarpare c nao, tale dekhi
00:09:55to result ki, aki rakam ase ki nai, je sabujta a, begunita b, ar kamulata c. Ami jodi ebar
00:10:01aage b nilam, erpare a nai, a mane sabujta, e je sabujta nai, prothome b nilam, tarpare
00:10:10a nilam, tarpare c nilam. Ebar dekhi to lobdhita ki ekdom aager moton hoi ki na? Jodi aager
00:10:17moton hoi, tahole to ami etake dhore ekhane basale, aki rakam result asbe. Dekhi to aki
00:10:21rakam ase ki na? E je aadi bindu ekhane basbe, ar ses bindu, oi dakho, ekdom parfectly mile
00:10:28gese. Parfectly mile gese. Accha, eta galo. Eibar, bolo to dekhi, aha, eta baro chota
00:10:37kara theek na. Eibar, jodi c plus a plus b kori. Arthaat prothome aage c vector nilam,
00:10:43prothome aage, accha ekhane theke ekhane unipo. E je aamadar c vector ta nilam, tarpare dhore
00:10:50a vector ke nilam, e je ekta sese sate aar ekta suru. Prothome c nilam, tarpare a nilam,
00:10:56tarpare b, tarpare b. Jodi aibhabe kore nai, tahole dekho to aamadar lobdhi konta hobe.
00:11:03Jodi lobdhi same hoye, tahole to eita diye hi prakash karte para aujit. Dekhi to mile
00:11:07ki na? Dekho to prothome taar aadi bindu, sathe jog kole, dakho, sesta ses bindu, ekdom
00:11:12perfectly mile jatche. Perfectly mile jatche. Etaar mane ki bojhaye? Etaar mane bojhaye,
00:11:20tumi jog jakhon karcho, takhon kon order e karcho, kontar pare konta jog karcho, se itar
00:11:28opare kintu result dependent na, se itar opare kintu result depend korbe na.
00:11:36So tahole, darao, ekta minute, et ekto booste thako, ekhoni aasche.
00:11:41Ok. Dekho, sunte parcho ki na? Sunte parcho sabai? Sunte parcho sabai? Ok, bujha ses.
00:12:05Sabai bujhchi? Sabai bujhchi? Dekho, je amra je bhabe kor e vector gula ke jog kori na keno,
00:12:13aage A B C hok, athoba B A C hok, athoba C A B hok, je bhabe hi hok na keno, protekta
00:12:21khetre hi amader kintu, jei lobdhita, seta eki rakam hotche. Eki rakam hotche. Thik
00:12:28ase? Clear? Bhitad diye gale lobdhi hobe, asobhitha nahi to. Lobdhita ke bhabe chinta
00:12:35karo, je saroner moton. Saron, jei tumi, mone karo, ei jaga theke prothome eto dur gela,
00:12:41tarpore e dike asla, tarpore e dike asla. Tehle saron konta? Adi theke ses, adi theke
00:12:47ses, to bhitad diye galo na, bairi diye galo, eita to amader jorno mandatory na. Thik ase?
00:12:53Dekho, khayal karo, vektor e jog karar somai kintu, dui rakam er niyam niyam na katha bolsi,
00:12:59ekto samari kore feli. Ekta chilo samantarik sutro, samantarik sutre somai amra ki kori
00:13:04balo to? Dui ta vektor er adi bindu ke ek bindute niye, tarpore, ekta samantarika ki?
00:13:11Tarpore, ekta samantarika ki? Ei samantarik er je karna ta hoye, se hi karna ta hotche
00:13:16amader lobdhi nirdesh karto. Eta chilo, samantarik sutro ta. Jei dui ta vektor er
00:13:21adi bindu ke, amra ge ek bindute ene, tarpore, ekta samantarik akbo, ebom tar je karna ta
00:13:27hobe, se ta lobdhi nirdesh korbe. Arakta niyam ki chilo? Sadharan sutro jeta, se ta ki chilo
00:13:33je, aneg bula vektor jodi amader kase thake, tahola amra ekta vektor er adi, arakta vektor
00:13:39e sese sata, arakta vektor e suru. Tarpore dharo, arakta vektor e suru sate, arakta vektor
00:13:44e sese sata, arakta suru. Ei bhabe kore jog kore, kore, kore, kore, amader adi theke ses
00:13:49por jonto, jei vektor ta pawa jabe, se ta hi hotse, ei tintar lobdhi vektor. Tai na?
00:13:54To dui rakam niyam, samantarik sutre some adi bindu ke ek bindute ana hoi silo, patch
00:13:59khaba na, khabar dhar, notun notun jakon parcho, takhon eta patch laga khub sahabi, kintu
00:14:03khyal rakhba. Jakon samantarik sutro ni amra parasuna karchi, takhon kintu samantarik sutre
00:14:08er khetre, vektor gular adi bindu ke ek bindute ante hoy, vektor gular adi bindu ke ek bindute
00:14:15ante hoy. Ar jakon amra sadharan sutro prayog kore lobdhi ber kotshi, takhon kintu ekta
00:14:21sese sata, arakta suru, ekta sese sata, arakta suru, ei bhabe kore amra lobdhi ber kori.
00:14:26Clear? E gula aage hi karaisi, kintu hi jaare bhai recap karte si, karan hoi jei aneke
00:14:31tu confused hai tar jor na. Theek ase? Butchi? Sahaj. Ok.
00:14:36Ta hole, amra eta boozlam, jei vektor bijgonit er khetre kintu binimoye sutro mene chale.
00:14:42Vektor bijgonit binimoye sutro mene chale.
00:14:45E baar asho sangjak sutro ba associative law.
00:14:48Eta ki bole? Associative law ta bole erokam, jei mone karo amar kase jodi duita vektor
00:14:55A plus B thake, eta onekta binimoye sutra er moton hi tumi chinta karte paro.
00:15:00Eta jeeta bole, jei tumi jodi A plus B duita vektor joke kore,
00:15:05tar sathe C vektor ke joke karo, ta hole result er mann ja hobe, tumi jodi A vektor
00:15:14er sathe B plus C er lobdhi ke joke karo, ta hole lobdhir mann eki rakam asbe.
00:15:21Ki bollo kathata? Dekho, je gula bracket e ase, jaman A plus B ekta bracket er moddhe
00:15:29A bracket er thaka mane hotse, A duita vektor er lobdhir sathe, C vektor er lobdhi karte bolthe.
00:15:37Eta lobdhir mann ja hobe, A plus B joke kore je result ta pavo, tar sathe C joke kore,
00:15:43jei lobdhi ta asbe, B plus C joke kore je mann ta pavo, tar sathe A joke kore,
00:15:49eki lobdhi pawa jabe. Chalo, eta abo amra ekto test kore dekhi,
00:15:53aswale ki yei sutrata khaate ki na?
00:15:57Boite proman ase, kentu proman lagbe na, tumi je bhabe visuali dekcho,
00:16:01eta hi tamar concept boostinge onek besi help kore.
00:16:05So dekho, prothome amra mone karo erokam ekta vektor nilam,
00:16:09eta hotse mone kollam amadir A vektor,
00:16:13tarpore dharo ekane arekta vektor nilam,
00:16:17eta hotse mone karo B vektor,
00:16:20tarpore dharo ekane arekta vektor nilam, eta hotse amadir C vektor.
00:16:24Pinta vektor erokam ase. Amadir ki bollo dekho,
00:16:28A ar B er jei lobdhi ta pachcho, A vektor
00:16:32ebong B vektor er jei lobdhi ta pachcho. Sono, egula khatai
00:16:36chobi saho aakte jeo na. Ami boli, khatai shudhu matro yei tuku lakha lakho.
00:16:40Khatai shudhu matro yei tuku lakha lakho. Tik ase?
00:16:44Khatai shudhu matro yei tuku lakha lakho. Chobi jai part tuku ase,
00:16:48eta tomar emni te hi mone thakbe. Karun tumi jokhon eta dekhba,
00:16:52klase jodi bujhe jao, tahole eta tomar chobi te ki chilo eta emni mone thakbe.
00:16:56Khatai ektu manojag diye shudhu dekho. Tik ase?
00:17:00Ek, ae sono, ei katha kokona jigesh karba na, je bhaiya,
00:17:04ei lektar karar junni ki aagerta kore asta hobi? Eta to avosh hoi ne baba.
00:17:08Sab samay amra ki bhabhe parachche? Amra to bitchin na bhabhe parachche na.
00:17:12Ekta sesh kare arekta. Tar opare bhitti kare arekta.
00:17:16Sababik. Ekhon tumi jodi amra ek katha bolo. Je bhai,
00:17:20ami onek talented. Ami jokhon bari banabo, ami do tala na banaye.
00:17:24Ami ki bhaiya, tin tala banate barbo? Ae, eta kono prashna holo?
00:17:28Bolo, eta kokono sambhav? Do tala na banaye, ekal tin tala banate barbe?
00:17:32Tin tala, kaz karlo, pilar bhalo moton gatlo na,
00:17:36chaat tala banate barbe? Parbe na. Tahole, ekta klas, arekta klas
00:17:40eropar dependent. Eta sab samayar junne satti. Kichu kichu khetre
00:17:44hai to ba, exception thakte pare. Kintu aigula ke amra chinta karuna.
00:17:48Example hi sebe nibuna. Sab samay johon klas karcho, chesta karba ager gula
00:17:52follow kare ese, tar pare karar channa. Gotcho?
00:17:56Ok. Theeka se.
00:18:00Dekho. Tahole, amadar prothome A are B vectorer
00:18:04jai lobdhi ta hotse, se lobdhi ta konta? Se lobdhi ta hotse, eta.
00:18:08Eta konta? Eta hotse amadar A are B vectorer lobdhi.
00:18:12Eta ke ame liklam, A vector ta hotse amadar A are B vectorer lobdhi.
00:18:16Ek jan bolso, bhaiya, A plus C kare ta sate B jog kola hobi ke na? Eki hobi. Eki result.
00:18:20Ekon dekho, eta hola amadar A plus B vector, tai na?
00:18:24A plus B vector. Tar sate ki korte bolse? C vector ke jog korte
00:18:28bolse. Aso jog kori. Tar sate aso C vector ke jog kori. Acha ekta minute.
00:18:32Dutar kalar eki rakom hoye gese. Etar kalar ta green kore deyi.
00:18:36Ta sate C vectorer lobdhi. Tale C vectorer lobdhi kole ki hobi?
00:18:40C vectorer lobdhi kole ayi dekho.
00:18:44Eta hotse chilo amadar A plus B vector. Khabaddar ebhabi likba na?
00:18:48Eta to shankhar jog na. Eta ki? Vector jog.
00:18:52Tale vector jog er jone A plus B liklam. Eta hotse C vector.
00:18:56Tale A plus B plus C. Tahole amadar lobdhi je manta hobe
00:19:00se ta konta? E jeta. A plus B er je lobdhi chilo, eta A plus B er
00:19:04lobdhi chilo, ta sate amra C vectorer lobdhi kore A output ta paise.
00:19:08Ekhon ekhane je lobdhi ta pela, amadar dekhate hobe
00:19:12A plus B plus C er soman kina? Tale bhai dekhi to B
00:19:16plus C mane, eta hotse B vector, eta hotse C vector.
00:19:20Ei to. Tale B plus C vectorer je lobdhi ta
00:19:24se ta konta, se ta hotse ei ta. Eta hotse amadar
00:19:28B vector chilo. Eta chilo amadar C vector. Tahole eta hotse
00:19:32B plus C vector. B plus C vector
00:19:36A vector
00:19:40A vector
00:19:44A plus B vector
00:19:48A vector
00:19:52A vector
00:19:56A vector
00:20:00A vector
00:20:04A vector
00:20:08A vector
00:20:12A vector
00:20:16A vector
00:20:20A vector
00:20:24A vector
00:20:28A vector
00:20:32A vector
00:20:36A vector
00:20:40A vector
00:20:44A vector
00:20:48A vector
00:20:52A vector
00:20:56A vector
00:21:00Very good. Very good.
00:21:04Clear. Eke bare clear. Bhaiya, jodi note na rekhe
00:21:08slide dekhe pari, problem hobe. Na, problem tumi aage note
00:21:12karba. Note karba. Tikase? Ekhon
00:21:16note karar bayas. Tikase? Ok.
00:21:20Acha, galo. Ebar asho
00:21:24bantan sutra, bar distributive law. Ei law ta
00:21:28kamon dekho. Ei law ta bolche.
00:21:32Ekola gintu sab.
00:21:36To boye sate mil paba.
00:21:40Tumadar ke asche?
00:21:48Dekho, eta ki bollam?
00:21:52Duita vector. A ebong B. Ekho na ashe nai? Very good.
00:21:56Dekho na ashe nai?
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00:25:56Dekho na ashe nai?
00:26:00Dekho na ashe nai?
00:26:04Dekho na ashe nai?
00:26:08Dekho na ashe nai?
00:26:12Dekho na ashe nai?
00:26:16Dekho na ashe nai?
00:26:20Dekho na ashe nai?
00:26:24Dekho na ashe nai?
00:26:28Dekho na ashe nai?
00:26:32Dekho na ashe nai?
00:26:36Dekho na ashe nai?
00:26:40Dekho na ashe nai?
00:26:44Dekho na ashe nai?
00:26:48Dekho na ashe nai?
00:26:52Dekho na ashe nai?
00:26:56Dekho na ashe nai?
00:27:00Dekho na ashe nai?
00:27:04Dekho na ashe nai?
00:27:08Dekho na ashe nai?
00:27:12Dekho na ashe nai?
00:27:16Dekho na ashe nai?
00:27:20Dekho na ashe nai?
00:27:24Dekho na ashe nai?
00:27:28Dekho na ashe nai?
00:27:32Dekho na ashe nai?
00:27:36Dekho na ashe nai?
00:27:40Dekho na ashe nai?
00:27:44Dekho na ashe nai?
00:27:48Dekho na ashe nai?
00:27:52Dekho na ashe nai?
00:27:56Dekho na ashe nai?
00:28:00Dekho na ashe nai?
00:28:04Dekho na ashe nai?
00:28:08Dekho na ashe nai?
00:28:12Dekho na ashe nai?
00:28:16Dekho na ashe nai?
00:28:20Dekho na ashe nai?
00:28:24Dekho na ashe nai?
00:28:28Dekho na ashe nai?
00:28:32Dekho na ashe nai?
00:28:36Dekho na ashe nai?
00:28:40Dekho na ashe nai?
00:28:44Dekho na ashe nai?
00:28:48Dekho na ashe nai?
00:28:52Dekho na ashe nai?
00:28:56Dekho na ashe nai?
00:29:00Dekho na ashe nai?
00:29:04Dekho na ashe nai?
00:29:08Dekho na ashe nai?
00:29:12Dekho na ashe nai?
00:29:16Dekho na ashe nai?
00:29:20Dekho na ashe nai?
00:29:24Dekho na ashe nai?
00:29:28Dekho na ashe nai?
00:29:32Dekho na ashe nai?
00:29:36Dekho na ashe nai?
00:29:40Dekho na ashe nai?
00:29:44Dekho na ashe nai?
00:29:48Dekho na ashe nai?
00:29:52Dekho na ashe nai?
00:29:56Dekho na ashe nai?
00:30:00Dekho na ashe nai?
00:30:04Dekho na ashe nai?
00:30:08Dekho na ashe nai?
00:30:12Dekho na ashe nai?
00:30:16Dekho na ashe nai?
00:30:20Dekho na ashe nai?
00:30:24Dekho na ashe nai?
00:30:28Dekho na ashe nai?
00:30:32Dekho na ashe nai?
00:30:36Dekho na ashe nai?
00:30:40Dekho na ashe nai?
00:30:44Dekho na ashe nai?
00:30:48Dekho na ashe nai?
00:30:52Dekho na ashe nai?
00:30:56Dekho na ashe nai?
00:31:00Dekho na ashe nai?
00:31:04Dekho na ashe nai?
00:31:08Dekho na ashe nai?
00:31:12Dekho na ashe nai?
00:31:16Dekho na ashe nai?
00:31:20Dekho na ashe nai?
00:31:24Dekho na ashe nai?
00:31:28Dekho na ashe nai?
00:31:32Dekho na ashe nai?
00:31:36Dekho na ashe nai?
00:31:40Dekho na ashe nai?
00:31:44Dekho na ashe nai?
00:31:48Dekho na ashe nai?
00:31:52Dekho na ashe nai?
00:31:56Dekho na ashe nai?
00:32:00Dekho na ashe nai?
00:32:04Dekho na ashe nai?
00:32:08Dekho na ashe nai?
00:32:12Dekho na ashe nai?
00:32:16Dekho na ashe nai?
00:32:20Dekho na ashe nai?
00:32:24Dekho na ashe nai?
00:32:28Dekho na ashe nai?
00:32:32Dekho na ashe nai?
00:32:36Dekho na ashe nai?
00:32:40Dekho na ashe nai?
00:32:44Dekho na ashe nai?
00:32:48Dekho na ashe nai?
00:32:52Dekho na ashe nai?
00:32:56Dekho na ashe nai?
00:33:00Dekho na ashe nai?
00:33:04Dekho na ashe nai?
00:33:08Dekho na ashe nai?
00:33:12Dekho na ashe nai?
00:33:16Dekho na ashe nai?
00:33:20Dekho na ashe nai?
00:33:24Dekho na ashe nai?
00:33:28Dekho na ashe nai?
00:33:32Dekho na ashe nai?
00:33:36Dekho na ashe nai?
00:33:40Dekho na ashe nai?
00:33:44Dekho na ashe nai?
00:33:48Dekho na ashe nai?
00:33:52Dekho na ashe nai?
00:33:56Dekho na ashe nai?
00:34:00Dekho na ashe nai?
00:34:04Dekho na ashe nai?
00:34:08Dekho na ashe nai?
00:34:12Dekho na ashe nai?
00:34:16Dekho na ashe nai?
00:34:20Dekho na ashe nai?
00:34:24Dekho na ashe nai?
00:34:28Dekho na ashe nai?
00:34:32Dekho na ashe nai?
00:34:36Dekho na ashe nai?
00:34:40Dekho na ashe nai?
00:34:44Dekho na ashe nai?
00:34:48Dekho na ashe nai?
00:34:52Dekho na ashe nai?
00:34:56Dekho na ashe nai?
00:35:00Dekho na ashe nai?
00:35:04Dekho na ashe nai?
00:35:08Dekho na ashe nai?
00:35:12Dekho na ashe nai?
00:35:16Dekho na ashe nai?
00:35:20Dekho na ashe nai?
00:35:24Dekho na ashe nai?
00:35:28Dekho na ashe nai?
00:35:32Dekho na ashe nai?
00:35:36Dekho na ashe nai?
00:35:40Dekho na ashe nai?
00:35:44Dekho na ashe nai?
00:35:48Dekho na ashe nai?
00:35:52Dekho na ashe nai?
00:35:56Dekho na ashe nai?
00:36:00Dekho na ashe nai?
00:36:04Dekho na ashe nai?
00:36:08Dekho na ashe nai?
00:36:12Dekho na ashe nai?
00:36:16Dekho na ashe nai?
00:36:20Dekho na ashe nai?
00:36:24Dekho na ashe nai?
00:36:28Dekho na ashe nai?
00:36:32Dekho na ashe nai?
00:36:36Dekho na ashe nai?
00:36:40Dekho na ashe nai?
00:36:44Dekho na ashe nai?
00:36:48Dekho na ashe nai?
00:36:52Dekho na ashe nai?
00:36:56Dekho na ashe nai?
00:37:00Dekho na ashe nai?
00:37:04Dekho na ashe nai?
00:37:08Dekho na ashe nai?
00:37:12Dekho na ashe nai?
00:37:16Dekho na ashe nai?
00:37:20Dekho na ashe nai?
00:37:24Dekho na ashe nai?
00:37:28Dekho na ashe nai?
00:37:32Dekho na ashe nai?
00:37:36Dekho na ashe nai?
00:37:40Dekho na ashe nai?
00:37:44Dekho na ashe nai?
00:37:48Dekho na ashe nai?
00:37:52Dekho na ashe nai?
00:37:56Dekho na ashe nai?
00:38:00Dekho na ashe nai?
00:38:04Dekho na ashe nai?
00:38:08Dekho na ashe nai?
00:38:12Dekho na ashe nai?
00:38:16Dekho na ashe nai?
00:38:20Dekho na ashe nai?
00:38:24Dekho na ashe nai?
00:38:28Dekho na ashe nai?
00:38:32Dekho na ashe nai?
00:38:36Dekho na ashe nai?
00:38:40Dekho na ashe nai?
00:38:44Dekho na ashe nai?
00:38:48Dekho na ashe nai?
00:38:52Dekho na ashe nai?
00:38:56Dekho na ashe nai?
00:39:00Dekho na ashe nai?
00:39:04Dekho na ashe nai?
00:39:08Dekho na ashe nai?
00:39:12Dekho na ashe nai?
00:39:16Dekho na ashe nai?
00:39:20Dekho na ashe nai?
00:39:24Dekho na ashe nai?
00:39:28Dekho na ashe nai?
00:39:32Dekho na ashe nai?
00:39:36Dekho na ashe nai?
00:39:40Dekho na ashe nai?
00:39:44Dekho na ashe nai?
00:39:48Dekho na ashe nai?
00:39:52Dekho na ashe nai?
00:39:56Dekho na ashe nai?
00:40:00Dekho na ashe nai?
00:40:04Dekho na ashe nai?
00:40:08Dekho na ashe nai?
00:40:12Dekho na ashe nai?
00:40:16Dekho na ashe nai?
00:40:20Dekho na ashe nai?
00:40:24Dekho na ashe nai?
00:40:28Dekho na ashe nai?
00:40:32Dekho na ashe nai?
00:40:36Dekho na ashe nai?
00:40:40Dekho na ashe nai?
00:40:44Dekho na ashe nai?
00:40:48Dekho na ashe nai?
00:40:52Dekho na ashe nai?
00:40:56Dekho na ashe nai?
00:41:00Dekho na ashe nai?
00:41:04Dekho na ashe nai?
00:41:08Dekho na ashe nai?
00:41:12Dekho na ashe nai?
00:41:16Dekho na ashe nai?
00:41:20Dekho na ashe nai?
00:41:24Dekho na ashe nai?
00:41:28Dekho na ashe nai?
00:41:32Dekho na ashe nai?
00:41:36Dekho na ashe nai?
00:41:40Dekho na ashe nai?
00:41:44Dekho na ashe nai?
00:41:48Dekho na ashe nai?
00:41:52Dekho na ashe nai?
00:41:56Dekho na ashe nai?
00:42:00Dekho na ashe nai?
00:42:04Dekho na ashe nai?
00:42:08Dekho na ashe nai?
00:42:12Dekho na ashe nai?
00:42:16Dekho na ashe nai?
00:42:20Dekho na ashe nai?
00:42:24Dekho na ashe nai?
00:42:28Dekho na ashe nai?
00:42:32Dekho na ashe nai?
00:42:36Dekho na ashe nai?
00:42:40Dekho na ashe nai?
00:42:44Dekho na ashe nai?
00:42:48Dekho na ashe nai?
00:42:52Dekho na ashe nai?
00:42:56Dekho na ashe nai?
00:43:00Dekho na ashe nai?
00:43:04Dekho na ashe nai?
00:43:08Dekho na ashe nai?
00:43:12Dekho na ashe nai?
00:43:16Dekho na ashe nai?
00:43:20Dekho na ashe nai?
00:43:24Dekho na ashe nai?
00:43:28Dekho na ashe nai?
00:43:32Dekho na ashe nai?
00:43:36Dekho na ashe nai?
00:43:40Dekho na ashe nai?
00:43:44Dekho na ashe nai?
00:43:48Dekho na ashe nai?
00:43:52Dekho na ashe nai?
00:43:56Dekho na ashe nai?
00:44:00Dekho na ashe nai?
00:44:04Dekho na ashe nai?
00:44:08Dekho na ashe nai?
00:44:12Dekho na ashe nai?
00:44:16Dekho na ashe nai?
00:44:20Dekho na ashe nai?
00:44:24Dekho na ashe nai?
00:44:28Dekho na ashe nai?
00:44:32Dekho na ashe nai?
00:44:36Dekho na ashe nai?
00:44:40Dekho na ashe nai?
00:44:44Dekho na ashe nai?
00:44:48Dekho na ashe nai?
00:44:52Dekho na ashe nai?
00:44:56Dekho na ashe nai?
00:45:00Dekho na ashe nai?
00:45:04Dekho na ashe nai?
00:45:08Dekho na ashe nai?
00:45:12Dekho na ashe nai?
00:45:16Dekho na ashe nai?
00:45:20Dekho na ashe nai?
00:45:24Dekho na ashe nai?
00:45:28Dekho na ashe nai?
00:45:32Dekho na ashe nai?
00:45:36Dekho na ashe nai?
00:45:40Dekho na ashe nai?
00:45:44Booste paasso?
00:45:48IJ kotha e galo?
00:45:52IJ hotse ek din aakashe ure berachchilo.
00:45:56Oke ami daklam. Ei, tui ure berachchis keno? Niche daam?
00:46:00O bolo na na bhai, amar urte hi bhal lagche. Toh is takhon theke se ure hi berachche.
00:46:04Ii jonna tumi IJ ke kakhon ho hi khuje baba na. Ii je ho, IJ har nai.
00:46:08Dekhechu? Eta hi hotse logic.
00:46:12IJ kotha e galo? IJ de toh amra vector ta ke prakash karchilam.
00:46:16Ekta vector er ki thake? Tar maan thake, tar dikh thake.
00:46:20Amra jokhon maan prakash karchi, tohkon ki are IJ
00:46:24cap thakbe? Vector thakbe tohkon? Na toh.
00:46:28Na toh. Tali ekane eta holo vector ta, tar maan ta hotse
00:46:32root over 3 square plus 4 e square. Sesh.
00:46:36Done, dana, done, done. Thik ase?
00:46:40Thik ase?
00:46:44Thik ase?
00:46:48Good, very good.
00:46:52Bhaiya, apnar class 2x speed e dekhar karone normal speed e booji na.
00:46:56Eta toh koh baro ekta rok. Tali tumi 2x speed e korba.
00:47:00Tumi 2x speed e korba.
00:47:04Asker lecture eto mazar.
00:47:08Ato shanti lagbe.
00:47:12Tumi chokbando kuro vector e katha chinta korba.
00:47:16Tar maani ki atokhon IJ chilo.
00:47:20Amra ekta tale ekta vector aksi.
00:47:24Ekta fakha jaigan modde ekta vector aksi.
00:47:28Dekho, munne kara amar kase 3 ta akho ase.
00:47:32Bishash karo, amar kase 3 ta akho ase.
00:47:36Eta hotse amadar x akho.
00:47:40Eta hotse amadar y akho.
00:47:44Eta hotse amadar z akho.
00:47:48Eta hotse amadar z akho.
00:47:52Eta hotse amadar z akho.
00:47:56Eta hotse amadar z akho.
00:48:00Eta hotse amadar z akho.
00:48:04E bhaiya, eto sundar chhobi.
00:48:08Kibhabe aaklen.
00:48:12Asole, pratibha dekhecho?
00:48:16Daag dile kohono baka hoyena.
00:48:20Ekdomi soja daag.
00:48:24Bhaba jaye kohono.
00:48:28Ki talent.
00:48:32Tumra kolle to aare kasto kare amar prasong samar kotta hai na.
00:48:36Taale bhaiya, eta mune kara amadar x akho.
00:48:40Eta hotse mune kara amadar y akho.
00:48:44Eta hotse amadar z akho.
00:48:48Eta hotse x y tal.
00:48:52Eta hotse tal.
00:48:56Eta hotse x y tal.
00:49:00Eta hotse x y tal.
00:49:04Eta hotse x y tal.
00:49:08Eta hotse x y tal.
00:49:12Eta hotse x y tal.
00:49:16Eta hotse x y tal.
00:49:20Eta hotse x y tal.
00:49:24Eta hotse x y tal.
00:49:28Eta hotse x y tal.
00:49:32Eta hotse x y tal.
00:49:36Eta hotse x y tal.
00:49:40Eta hotse x y tal.
00:49:44Eta hotse x y tal.
00:49:48Eta hotse x y tal.
00:49:52Eta hotse x y tal.
00:49:56Eta hotse x y tal.
00:50:00Eta hotse x y tal.
00:50:04Eta hotse x y tal.
00:50:08Eta hotse x y tal.
00:50:12Eta hotse x y tal.
00:50:16Eta hotse x y tal.
00:50:20Eta hotse x y tal.
00:50:24Eta hotse x y tal.
00:50:28Eta hotse x y tal.
00:50:32Eta hotse x y tal.
00:50:36Eta hotse x y tal.
00:50:40Eta hotse x y tal.
00:50:44Eta hotse x y tal.
00:50:48Eta hotse x y tal.
00:50:52Eta hotse x y tal.
00:50:56Eta hotse x y tal.
00:51:00Eta hotse x y tal.
00:51:04Eta hotse x y tal.
00:51:08Eta hotse x y tal.
00:51:12Eta hotse x y tal.
00:51:16Eta hotse x y tal.
00:51:20Eta hotse x y tal.
00:51:24Eta hotse x y tal.
00:51:28Eta hotse x y tal.
00:51:32Eta hotse x y tal.
00:51:36Eta hotse x y tal.
00:51:40Eta hotse x y tal.
00:51:44Eta hotse x y tal.
00:51:48Eta hotse x y tal.
00:51:52Eta hotse x y tal.
00:51:56Eta hotse x y tal.
00:52:00Eta hotse x y tal.
00:52:04Eta hotse x y tal.
00:52:08Eta hotse x y tal.
00:52:12Eta hotse x y tal.
00:52:16Eta hotse x y tal.
00:52:20Eta hotse x y tal.
00:52:24Eta hotse x y tal.
00:52:28Eta hotse x y tal.
00:52:32Eta hotse x y tal.
00:52:36Eta hotse x y tal.
00:52:40Eta hotse x y tal.
00:52:44Eta hotse x y tal.
00:52:48Eta hotse x y tal.
00:52:52Eta hotse x y tal.
00:52:56Eta hotse x y tal.
00:53:00Eta hotse x y tal.
00:53:04Eta hotse x y tal.
00:53:08Eta hotse x y tal.
00:53:12Eta hotse x y tal.
00:53:16Eta hotse x y tal.
00:53:20Eta hotse x y tal.
00:53:24Eta hotse x y tal.
00:53:28Eta hotse x y tal.
00:53:32Eta hotse x y tal.
00:53:36Eta hotse x y tal.
00:53:40Eta hotse x y tal.
00:53:44Eta hotse x y tal.
00:53:48Eta hotse x y tal.
00:53:52Eta hotse x y tal.
00:53:56Eta hotse x y tal.
00:54:00Eta hotse x y tal.
00:54:04Eta hotse x y tal.
00:54:08Eta hotse x y tal.
00:54:12Eta hotse x y tal.
00:54:16Eta hotse x y tal.
00:54:20Eta hotse x y tal.
00:54:24Eta hotse x y tal.
00:54:28Eta hotse x y tal.
00:54:32Eta hotse x y tal.
00:54:36Eta hotse x y tal.
00:54:40Eta hotse x y tal.
00:54:44Eta hotse x y tal.
00:54:48Eta hotse x y tal.
00:54:52Eta hotse x y tal.
00:54:56Eta hotse x y tal.
00:55:00Eta hotse x y tal.
00:55:04Eta hotse x y tal.
00:55:08Eta hotse x y tal.
00:55:12Eta hotse x y tal.
00:55:16Eta hotse x y tal.
00:55:20Eta hotse x y tal.
00:55:24Eta hotse x y tal.
00:55:28Eta hotse x y tal.
00:55:32Eta hotse x y tal.
00:55:36Eta hotse x y tal.
00:55:40Eta hotse x y tal.
00:55:44Eta hotse x y tal.
00:55:48Eta hotse x y tal.
00:55:52Eta hotse x y tal.
00:55:56Eta hotse x y tal.
00:56:00Eta hotse x y tal.
00:56:04Eta hotse x y tal.
00:56:08Eta hotse x y tal.
00:56:12Eta hotse x y tal.
00:56:16Eta hotse x y tal.
00:56:20Eta hotse x y tal.
00:56:24Eta hotse x y tal.
00:56:28Eta hotse x y tal.
00:56:32Eta hotse x y tal.
00:56:36Eta hotse x y tal.
00:56:40Eta hotse x y tal.
00:56:44Eta hotse x y tal.
00:56:48Eta hotse x y tal.
00:56:52Eta hotse x y tal.
00:56:56Eta hotse x y tal.
00:57:00Eta hotse x y tal.
00:57:04Eta hotse x y tal.
00:57:08Eta hotse x y tal.
00:57:12Eta hotse x y tal.
00:57:16Eta hotse x y tal.
00:57:20Eta hotse x y tal.
00:57:24Eta hotse x y tal.
00:57:28Eta hotse x y tal.
00:57:32Eta hotse x y tal.
00:57:36Eta hotse x y tal.
00:57:40Eta hotse x y tal.
00:57:44Eta hotse x y tal.
00:57:48Eta hotse x y tal.
00:57:52Eta hotse x y tal.
00:57:56Eta hotse x y tal.
00:58:00Eta hotse x y tal.
00:58:04Eta hotse x y tal.
00:58:08Eta hotse x y tal.
00:58:12Eta hotse x y tal.
00:58:16Eta hotse x y tal.
00:58:20Eta hotse x y tal.
00:58:24Eta hotse x y tal.
00:58:28Eta hotse x y tal.
00:58:32Eta hotse x y tal.
00:58:36Eta hotse x y tal.
00:58:40Eta hotse x y tal.
00:58:44Eta hotse x y tal.
00:58:48Eta hotse x y tal.
00:58:52Eta hotse x y tal.
00:58:56Eta hotse x y tal.
00:59:00Eta hotse x y tal.
00:59:04Eta hotse x y tal.
00:59:08Eta hotse x y tal.
00:59:12Eta hotse x y tal.
00:59:16o b vector
00:59:20o b vector
00:59:24o b
00:59:28o b square
00:59:32o a square plus a b square
00:59:36o a square
00:59:40o a b square
00:59:44o b square
00:59:48root over x square plus y square
00:59:52plus z square
00:59:56root over x square plus y square plus z square
01:00:00I am not able to understand.
01:00:04Shortcut
01:00:08Someone told me
01:00:12Vector
01:00:16x y z
01:00:20x y z
01:00:24x y z
01:00:28x y z
01:00:32x y z
01:00:36x y z
01:00:40vector x, y, z vector x i cap plus y j cap plus z k cap, this is our positional vector.
01:00:51So, this is our positional vector x i cap plus y j cap plus z k cap. So, this is our positional
01:00:58vector x i cap plus y j cap plus z k cap. So, this is our positional vector x i cap plus
01:01:05y j cap plus z k cap. So, this is our positional vector x i cap plus y j cap plus z k cap. So,
01:01:12this is our positional vector x i cap plus y j cap plus z k cap. So, this is our positional
01:01:19vector x i cap plus z k cap. So, this is our positional vector x i cap plus y j cap plus
01:01:26z k cap. So, this is our positional vector x i cap plus z k cap. So, this is our positional
01:01:33vector x i cap plus z k cap. So, this is our positional vector x i cap plus z k cap. So,
01:01:40this is our positional vector x i cap plus z k cap. So, this is our positional vector
01:01:48x i cap plus z k cap. So, this is our positional vector x i cap plus z k cap. So, this is our
01:02:00positional vector x i cap plus z k cap. So, this is our positional vector x i cap plus
01:02:08z k cap. So, this is our positional vector x i cap plus z k cap. So, this is our positional
01:02:23vector x i cap plus z k cap. So, this is our positional vector x i cap plus z k cap.
01:02:38So, this is our positional vector x i cap plus z k cap. So, this is our positional vector
01:02:50x i cap plus z k cap. So, this is our positional vector x i cap plus z k cap. So, this is our
01:02:57positional vector x i cap plus z k cap. So, this is our positional vector x i cap
01:03:04vector 3i cap plus 4j cap plus 5k cap. Mole vector divided by 3 square plus 4 square plus
01:03:554 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:04:02square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:04:094 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:04:16square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:23plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:30plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:35plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:40plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:45plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:50plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:04:57plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:02plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:07plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:12plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:17plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:22plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:27plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:32plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:37plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:42plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:47plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:52plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:05:57plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:02plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:07plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:11plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:16plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:21plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:26plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:31plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:36plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:40plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:45plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:50plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:06:55plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:00plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:05plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:09plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:14plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:19plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:24plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:29plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:34plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:38plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:43plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:48plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:53plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:07:58plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:03plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:07plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:12plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:17plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:22plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:27plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:32plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:36plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:41plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:46plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:51plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:08:56plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:01plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:05plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:10plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:15plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:20plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:25plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:30plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:34plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:39plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:44plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:49plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:54plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:09:59plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:03plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:08plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:13plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:18plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:23plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:28plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:33plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:38plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:43plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:48plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:10:53plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:10:574 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:11:02square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:11:07plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:11:124 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:11:17square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:11:22plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:11:264 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:11:31square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:11:36plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:11:414 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:11:46square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:11:51plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:11:564 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:12:01square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:12:06plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:12:114 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:12:16square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:12:20plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:12:25plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:12:304 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:12:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:12:40plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:12:454 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:12:49plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:12:544 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:12:59square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:13:04plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:13:094 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:13:14square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:13:18plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:13:234 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:13:28square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:13:33plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:13:384 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:13:43square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:13:47plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:13:524 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:13:57square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:14:02plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:14:074 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:14:12square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:14:16plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:14:214 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:14:26square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:14:31plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:14:364 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:14:41square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:14:45plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:14:50plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:14:554 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:15:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:15:05plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:15:104 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:15:14plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:15:194 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:15:24square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:15:29plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:15:344 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:15:39square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:15:43plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:15:484 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:15:53square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:15:58plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:16:034 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:16:08square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:16:13plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:16:184 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:16:23square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:16:28plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:16:334 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:16:37plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:16:424 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:16:47square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:16:52plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:16:574 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:17:02plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:17:06square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:17:11plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:17:164 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:17:21square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:17:26plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:17:314 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:17:36square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:17:41plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus
01:17:464 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:17:51square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square
01:17:56plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:18:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:19:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:20:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:21:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:22:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:23:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:10square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:15square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:20square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:25square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:30square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:35square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:40square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:45square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:50square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:24:55square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:00square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:05square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:09square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:14square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:19square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:24square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:29square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:34square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:39square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:44square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:49square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:54square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:25:59square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:04square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:09square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:14square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:19square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:24square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:29square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:34square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:39square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:44square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:49square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:54square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:26:59square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:04square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:09square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:14square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:19square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:24square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:29square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:34square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:39square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:44square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:49square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:54square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:27:59square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:28:04square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:28:09square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:28:14square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:28:19square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
01:28:24square plus 4 square plus 4 square plus 4 square plus 4 square plus 4 square plus 4
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