HSC26free
HSC26free
  • 4 months ago
Transcript
00:00:30Hello, assalamu alaikum, sabai ke, ek tu janao to sound sunte batsho ki na, dekhte batsho
00:00:58ki na, hello, hello, tukor sound, jha chok choke sound achche, sounder thalai, ami to
00:01:10sunte batsho ki na, sundar sound, kono samosya nahi, jha dekhta bise na, so dekhi aage,
00:01:36so asha kari clear, sabai sunte batsho, amra ekhoni suru kore dibo, so sabai khata kolam
00:02:03ber karo, amra achke vector er chaat number klas nebo, abong achke amra shole aage din
00:02:09klas e je theory gula shiksilam, se hi gular math problem aachke amra solve korbo, anek
00:02:13anek math problem thakbe achke, theek ase, anek din par tamade shate abar dakha, to chalo
00:02:20amra tahole suru kori, hain, amra tahole suru kori, suno, achke amra je hi to anek kula
00:02:26math problem korbo, tamader kache ekta guide line thakbe, guide line ta hochche, jakhon
00:02:32problem gula solve korbo, anek mcq problem aachke, bootcho, anek gula mcq problem aachke
00:02:38aase, to, ay mcq problem, tumi jodi life class ek khata e tulte jao, tha hole ashole cover
00:02:45kore utte par bana, to se zorno ki korba boli, jakhon mcq gula dekba, takhon khyal korba
00:02:51amra ekhone pdf er page number dawa ase, ekhone page number dawa ase 20, tahole tumi jakhon
00:02:57khata e tulba, jai to koi lakha laguk, tumi takhon just paase 20 likhe, er pare hochche
00:03:04uttar ta likhe diba, ay mcq gula khata e kintu tulte jaba na khali khali, jai gula mone habe
00:03:10ekto kothin, ba jai gula mone habe na abhay aaye ta ekto ekto boro, sei gula tumi pare
00:03:15likte paro, ekto faka jaega rekhe, takhon likte paro, kintu mcq number ekhane itsa kare
00:03:20deyini, karon tahole khuje pawa jaye na, ortheke tumi jodi pdf er page number ta dekhe lakho,
00:03:26tale jakhon pdf ta hi scroll karwa, takhon booste parwa, o achche, 20 number page e,
00:03:30ei math ta chilo, thikase, ok, to, lecture 3 na khole ke aaj ke klas bujhbo, na, lecture
00:03:393 asole amra aager din jeta nilam, oye lecture 3 er opore asole aaj ke klas ta math practice,
00:03:46to e junno aager din er klas ta kara thaka lagbe, thikase, ok, so sabhai khata kolam
00:03:52niye ready thako, sathe calculator rekho, amra chalo tahole math problem suru kori,
00:03:58so jodi web app e problem hoye, web app e problem hoye, tahole chole asho, amra yate,
00:04:04ei facebook e chole asho, thikase, mcq gula note karar darkan nahi, je gula note kara
00:04:08lagbe, am bole dibo, thikase, klas emni tumi jodi theory gula bhalo maton note karo, tahole
00:04:14ar alada kare mcq note karar darkan nahi, kintu je gula am ekto important, se gula dagaye
00:04:19dibo, oye gula ekto note kare niba, thaila hi habe, thikase, ekto janao to web app e jara
00:04:24asho, na na am facebook e comment dekhbo, asubidha nahi, facebook e je pasa pasa hi
00:04:29comment ase, kona asubidha nahi, web app e jara aso ekto janao to, thikase ki na,
00:04:34hain, thikase, clear ase, to jade samushra hotse, tumra kindly facebook e chole asho,
00:04:39kindly facebook e chole asho, ok, so amra deri na kore, chalo ekho ni suru kore dibo,
00:04:45ekho ni suru kore dibo, sabhai khata kolam ready rakho, sabhai khata kolam ready rakho,
00:04:51ok, thik ase, thaila prothome amra asho lobdhir, sarbat chaman abang sarbonimno man,
00:04:59e gula ag ekto dekhe nahi, sarbat chaman, dekho agar din amra jai sutra shikhe chila,
00:05:04just ekto chotto recap kore feli, karo naton dinar para je hetu, amra jodi ekto recap kore feli,
00:05:10thaile sabar mathate ekdom brand new bhabhe abar sabkicho chole ashbe,
00:05:14so mane kolam, eita holo amadera ekta p vector, eita hotse amadera ekta q vector,
00:05:18ebong ei p aur q doita vector er moddhobarti jei cone ta,
00:05:23sei cone ta hotse mane kolam theeta, hei, sei cone ta mane kolam theeta,
00:05:27eita alpha hote pare, theeta hote pare, ekak boite ekak bhabe kora ase,
00:05:31eta niye kono chinta kor bana, just notation jodi theeta hai, thaile sutra kamon habe,
00:05:35seita amra likbo, ei doita vector er moddhobarti jei lobdheeta,
00:05:39sei lobdheeta mane kolam eita, lobdheeta hotse giye r vector,
00:05:44ebong amra ei lobdheeta jai maan, sei maan er ekta sutra shikhe chila,
00:05:49maan er sutra chilo erokom, jai r e square soman soman hobe,
00:05:53p square plus, q e square plus, 2 p q cos theeta, 2 p q cos theeta,
00:06:02ekane theeta ar parichoy ki, theeta ar parichoy chilo p r q er moddhobarti kon,
00:06:07theeta ar parichoy chilo p r q er moddhobarti kon,
00:06:11ekon khyal karo, jodi ami ekane r er value ta maximum chai,
00:06:15r er value jodi maximum pete chai, amar to p er maan constant, q er maan constant,
00:06:21jodi amke bole jei doita vector er moddhe kon kato hole lobdheer maan sarbaccho,
00:06:28kato degree kon er jone lobdheer maan sarbaccho habe,
00:06:32tahole bolo to p e q ke to ami dhodte parbo na,
00:06:35tale kato kon er jone r er maan ta sarbaccho habe,
00:06:39eta jodi ber karte chai, tahole ki amke cos theeta ar maan ta ho,
00:06:42thik maximum basate habe, tale cos theeta ar maximum maan kato hoi,
00:06:47cos theeta ar maximum maan amra jaani kintu plus one,
00:06:51ebong se ta takhoni sambhav, johan theeta er maan kato degree hoi,
00:06:55zero degree hoi, tahole ekane amra,
00:06:58jodi theeta ar maan ta zero degree basai,
00:07:01tahole ekane jeta ase,
00:07:03je r e square soman soman,
00:07:05dekho root over just p e square p e square plus two p q,
00:07:09karan cos theeta ar maan one hoye gese, one hoye gese,
00:07:12tale ekante ke amare jeta ase, se ta ki,
00:07:14je p plus q, p plus q whole square, karan eta a plus b whole square sutro,
00:07:21ekante ke amra r er maan ta kintu ber kore fel silam,
00:07:24r er maan ta hotse p plus q,
00:07:26ebong eita hi chilo amare duita vektor er sarbaccho je maan se ta,
00:07:31eta holo lobdhir sarbaccho maan,
00:07:34eta ki,
00:07:35eta hotse lobdhir sarbaccho maan,
00:07:39sarbaccho maan,
00:07:41tar maane,
00:07:43johan duita vektor eki dike kach kare,
00:07:46takhoni kintu amare total lobdhita sabchaite besi hoi,
00:07:51to mone karo jodi duita vektor ekta ek dike kach karche,
00:07:55arakta mone kollam ek dike kach karche,
00:07:57amon bhabe jodi duita vektor kach kare,
00:07:59tahole tader ja lobdhi hobe,
00:08:02lobdhir maan takhon barbe,
00:08:05lobdhir maan takhon barbe,
00:08:06jodi duita direction eki dike thake,
00:08:09duita vektor er direction jodi eki dik barabar thake,
00:08:14eki dik barabar thake,
00:08:15takhoni kintu tader duita vektor er jogfal,
00:08:19ba lobdhir maan sabchaite ki hobe,
00:08:21besi hobe,
00:08:22jato besi angle baate thake,
00:08:24amra dekhbo,
00:08:25jato besi angle baate thake,
00:08:26tato astaste lobdhir maan kintu komte thake,
00:08:30tahole sarbochcha maan kakhon hobe,
00:08:32jakhon duita vektor er moddho borti konta hobe 0 degree,
00:08:36jakhon duita vektor er moddho borti konta hobe 0 degree,
00:08:38takhoni amra kintu lobdhir sarbochcha maan pabho,
00:08:41takhoni amra lobdhir sarbochcha maan pabho,
00:08:44very good,
00:08:45thik ase galo,
00:08:46er pare aso sarbonimno maan,
00:08:49sarbonimno maan ta kakhon ase,
00:08:51je amra jodi duita vektor p aur q thake,
00:08:54tahole r e square saman saman hotche,
00:08:57p square plus,
00:08:58q e square plus,
00:09:002 p q cos theta,
00:09:03tahole eki bhabe,
00:09:05je moddho borti kon kata hole,
00:09:07lobdhir maan ta minimum hobe,
00:09:09moddho borti kon kata hole,
00:09:11lobdhir maan ta minimum hobe,
00:09:13tale r minimum hote hole,
00:09:15cos theta maan ta minimum lagbe,
00:09:17amra ki jaani bhai,
00:09:18cos theta maan minimum hoi kakhon,
00:09:21cos theta maan minimum hoi kato,
00:09:23minus 1 e na,
00:09:24tahole kakhon eta hoi,
00:09:26jakhon theta maan hoi 180 degree,
00:09:29180 degree,
00:09:31takhoni kinto amra dekho,
00:09:33ekane lobdhir je maan ta pabho,
00:09:36lobdhir je hi maan ta pabho,
00:09:38se ta ki hobe,
00:09:39cos 180 degree maan basale,
00:09:42eta ki hoye jabe,
00:09:43just minus 1 hoye jabe,
00:09:45cos theta maan minus 1 basale,
00:09:46e rokum ekta sutra asbe,
00:09:48tale takhon amra lekte parbo,
00:09:50p minus q hole square,
00:09:52ekane hotse r square,
00:09:54tale r er je maan eta hotse,
00:09:56p abom q er moddhe je biyog falta,
00:09:59se ita nirdesh kare,
00:10:01tale eta hi kinto lobdhir sarbonimno maan,
00:10:03eta hi ki,
00:10:04eta hi hotse lobdhir ta sarbonimno maan,
00:10:09sabche kam maan,
00:10:11tar maani ki,
00:10:12je ekta bostur opore,
00:10:14jakhon amadher duita bal kach korbe,
00:10:17takhon lobdhir maan ta,
00:10:18takhon hi sabche ite kam hobe,
00:10:19jakhon edher moddhabar tikon kato,
00:10:21180 degree,
00:10:23suppose eta jodi hoye 8 newton,
00:10:25eta jodi hoye 6 newton,
00:10:27takhon hi kinto sabche kam je hi maan ta,
00:10:29se ta 2 newton kach korbe,
00:10:31ar sabche besi je hi maan ta,
00:10:32se ta kato hobe,
00:10:33se ta hobe 8 ar 6 jog kare,
00:10:35je 14 hoye se ta,
00:10:36tahole dekho,
00:10:37amra jodi range dekte payi,
00:10:40je jakhon amra lobdhir maan er katha bolchi,
00:10:44ar p ebon q amarkase duita vektor ase,
00:10:48p ebon q amarkase duita vektor ase,
00:10:51tale bolo to lobdhir je hi maan ta,
00:10:53se hi lobdhir maan,
00:10:55jodi ekta range er moddhome amra prakash korte chai,
00:10:58tahole eta ki kibhabe prakash korbo,
00:11:00khayal karo lobdhir maan,
00:11:02amadher kinto sabche besi hote pare,
00:11:04p plus q jog kare ja hoye,
00:11:06tar soman,
00:11:07athoba tar theke choto hote pare,
00:11:09ebon sabche ite choto hote pare kar,
00:11:12p minus q er,
00:11:14p minus q er,
00:11:16karon ki,
00:11:17je eta sarbonimno maan,
00:11:19er soman hobe,
00:11:20athoba lobdhir maan ta,
00:11:22ye je lobdhir maan ta,
00:11:24sarbonimno maan er theke,
00:11:25baro maan er hobe,
00:11:27ar sarbocho maan er theke,
00:11:30choto maan er hobe,
00:11:31ba sarbocho maan er soman hobe,
00:11:33tahole,
00:11:33eta kinto amadher lobdhir range budhache,
00:11:37range budhache,
00:11:38tale amake bolo to dekhi,
00:11:40jodi kono ekta vektor thake,
00:11:41p vektor,
00:11:43jar maan hotse 8 newton,
00:11:45ebon kono ekta vektor ase,
00:11:47q vektor,
00:11:48jar maan hotse 6 newton,
00:11:50bolo to amadher lobdhir maan ta ki,
00:11:5315 newton hote parbe,
00:11:55bolo to 15 newton ki hote parbe,
00:11:58lobdhir maan ta ki 15 newton hote parbe,
00:12:01ba 1 newton ki hote parbe,
00:12:03bolo to,
00:12:04parbe na,
00:12:0515 newton kinto hote parbe na,
00:12:081 newton hote parbe na,
00:12:10keno,
00:12:10karun amadher ekane dekhte parcho,
00:12:122 ta vektor er maan theke parishkar budhache,
00:12:16je,
00:12:17amadher sarbocho maan hote pare kato,
00:12:198 ar choy jog kolle,
00:12:21lobdhir je maan ta,
00:12:228 ar choy jog kolle,
00:12:2414 soman hote pare,
00:12:25ba tar theke,
00:12:26choto hote pare,
00:12:27ar,
00:12:282 newton er soman hote pare,
00:12:29ba tar theke,
00:12:30boro hote pare,
00:12:31tahole,
00:12:32ei range er modhe kinto amadher lobdhir maan ta,
00:12:34thakbe,
00:12:35lobdhir maan ta,
00:12:36thakbe,
00:12:37ei range er modhe,
00:12:38kinto kakhone 15 newton hawa sambhob na,
00:12:411 newton hawa sambhob na,
00:12:43ar ekta information,
00:12:45tumi dekho,
00:12:46cos thetar je maan ta,
00:12:48cos thetar je maan ta,
00:12:50se cos thetar maan,
00:12:52bolo to dekhi,
00:12:54ekane,
00:12:56cos thetar je value,
00:12:58bolo to thetar maan briddhi pawar sate sate,
00:13:00jodi ami cos thetar maan soman x dhare nahi,
00:13:02suppose,
00:13:04thetar maan jato briddhi paaye,
00:13:060 theke johon 180,
00:13:08180 er modhe ghura phera kare,
00:13:10takhone bolo to,
00:13:12x er je maan ta,
00:13:14se x er maan ki barte thake na,
00:13:16kumte thake bolo to,
00:13:18thetar maan jato briddhi paaye,
00:13:20cos thetar maan kinto,
00:13:22tato astaste ki hoye,
00:13:24rash paye,
00:13:26tumi jodi graph ta ho khayal karo,
00:13:28kiser graph abar,
00:13:30kiser graph abar,
00:13:32je amra jodi thetar sathe,
00:13:34je thetar briddhi sate sate,
00:13:36thetare se graph ta kyamon hoye,
00:13:38graph ta ki,
00:13:40ayi rokum type er ekta graph hoye na,
00:13:42amon type er ekta graph hoye na,
00:13:44cos thetar graph,
00:13:46thetar sate sate,
00:13:48cos er value ta ebhabe kare change hoye,
00:13:50ebong eta hotse amade se plus one,
00:13:52tarpore,
00:13:54ayi deke jai value ta,
00:13:56eta hotse amade minus one,
00:13:58eta hotse zero,
00:14:00to dekho,
00:14:02amade johon thetar maan ta zero degree,
00:14:04johon thetar maan one,
00:14:06thetar maan johon ninety degree,
00:14:08tokon cos thetar maan kato zero,
00:14:10thetar maan johon ekso ashi degree,
00:14:12tokon ekso ashi degree,
00:14:14tokon amader cos thetar maan kato minus one,
00:14:16tale khayal kare dekho,
00:14:18e graph theke kintu clear,
00:14:20je amra johon thetar maan zero degree theke,
00:14:22thetar maan zero degree theke,
00:14:24johon ekso ashi degree hotse,
00:14:26tokon dekho,
00:14:28cos thetar maan ta aste aste aste ki hotse,
00:14:30komse komse zero hoye galo,
00:14:32tale zero degree theke,
00:14:34ekso ashi modhe kintu cos thetar maan aste aste aste ki hoye,
00:14:36komte thake,
00:14:38tahole amar jai sutro ase,
00:14:40je r soman soman root over,
00:14:42r soman soman root over,
00:14:44p square plus,
00:14:46q square plus,
00:14:482 p q cos theta,
00:14:50tale bhaiya bolo to dekhi,
00:14:52thetar maan jato baraba,
00:14:54cos thetar maan tato kombe,
00:14:56tale 2 p u cos theta,
00:14:58e purata maan aste aste komle,
00:15:00arar maan ki hoye,
00:15:02lobdhir maan aste aste ki hoye,
00:15:04komte thakbe na,
00:15:06tale amre ekhan the keo clearly buste pallam,
00:15:08thetar maan jodi barte thake,
00:15:10tale lobdhir maan ki hote thakbe,
00:15:12komte thakbe aste aste,
00:15:14thetar maan barte thakle,
00:15:16lobdhir maan komte thakbe aste aste,
00:15:18buste barso,
00:15:20thetar maan barte thakle,
00:15:22lobdhir maan aste aste komte thakbe,
00:15:24ami board e jaa kisu likbo,
00:15:26segula khataye tulba,
00:15:28already,
00:15:34written proshno jodi likte boli tokon likba,
00:15:36jodi na likte boli tale,
00:15:38prishta number ta likhe,
00:15:42tale amre eta ekhan the ke buslam,
00:15:44ekhon asho,
00:15:46eta ekto fizikali dekhar cheshta kari graph,
00:15:48maane yad yake chhobi yake,
00:15:50mane karo amade duita vector,
00:15:52ekta vector hotse eta p,
00:15:54ebong,
00:15:56arakta vector dehi darau,
00:15:58arakta vector dehi,
00:16:00jai vector ta hotse ehi rakam,
00:16:02jai vector ta,
00:16:04jai rakam ekto choto vector aklam,
00:16:06erakam ekta choto vector aklam,
00:16:08ekto bozhar cheshta kar,
00:16:10darun kicho idea ase ekhane,
00:16:12bolo to edher maddho borti kon kato,
00:16:14ekso ashi degree,
00:16:16edher maddho borti kon ki ekso ashi degree,
00:16:18na ki zero degree,
00:16:20zero degree karun duita eki dike kach kotshe,
00:16:22jodi dekhtam,
00:16:24ektar biparit,
00:16:26takhon ami boltam,
00:16:28tader parasparar maddho borti kon hotse,
00:16:30ekso ashi degree,
00:16:32kinto ekhane tader maddho borti kon kato degree,
00:16:34zero degree, very good,
00:16:36ekhon khayal karo to,
00:16:38duita vector er maddho borti kon,
00:16:40jodi ekhane zero degree hoi,
00:16:42tahole amra duita vector lobdi jakon karbo,
00:16:44lobdi jakon karbo,
00:16:46takhon hi lobdi ta ki habe,
00:16:48lobdi ta ki habe,
00:16:50mane karo,
00:16:52lobdi ta ki habe,
00:16:54lobdi ta ki habe,
00:16:56lobdi ta ki habe,
00:16:58lobdi ta ki habe,
00:17:00lobdi ta ki habe,
00:17:02lobdi ta ki habe,
00:17:04lobdi ta ki habe,
00:17:06lobdi ta ki habe,
00:17:08lobdi ta ki habe,
00:17:10lobdi ta ki habe,
00:17:12lobdi ta ki habe,
00:17:14lobdi ta ki habe,
00:17:16lobdi ta ki habe,
00:17:18lobdi ta ki habe,
00:17:20lobdi ta ki habe,
00:17:22lobdi ta ki habe,
00:17:24lobdi ta ki habe,
00:17:26lobdi ta ki habe,
00:17:28lobdi ta ki habe,
00:17:30lobdi ta ki habe,
00:17:32lobdi ta ki habe,
00:17:34lobdi ta ki habe,
00:17:36lobdi ta ki habe,
00:17:38lobdi ta ki habe,
00:17:40lobdi ta ki habe,
00:17:42lobdi ta ki habe,
00:17:44lobdi ta ki habe,
00:17:46lobdi ta ki habe,
00:17:480 degree
00:17:500 degree
00:17:520 degree
00:17:540 degree
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00:17:580 degree
00:18:000 degree
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00:18:080 degree
00:18:100 degree
00:18:120 degree
00:18:140 degree
00:18:160 degree
00:18:180 degree
00:18:200 degree
00:18:220 degree
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00:18:360 degree
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00:18:580 degree
00:19:000 degree
00:19:020 degree
00:19:040 degree
00:19:060 degree
00:19:080 degree
00:19:100 degree
00:19:120 degree
00:19:140 degree
00:19:160 degree
00:19:180 degree
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00:19:260 degree
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00:19:360 degree
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00:19:540 degree
00:19:560 degree
00:19:580 degree
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00:20:020 degree
00:20:040 degree
00:20:060 degree
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00:20:120 degree
00:20:140 degree
00:20:160 degree
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00:32:44So, if you take the first vector and the second vector, which one will be shifted?
00:32:51If the values of the two vectors are same, then the value of this vector is 10 Newton
00:32:58and the value of this vector is 10 Newton.
00:33:01If this is the case, then which side of the vector will be equal?
00:33:05Which side will be shifted?
00:33:07The middle side.
00:33:08The middle side.
00:33:09The middle side will be equal to 1 to 12.
00:33:11But if the value is two times, then which one will be equal?
00:33:17Here even if it is three times, than it will be equal to three Newton.
00:33:24Why?
00:33:25Because if there was one part which was more, then it becomes 12 Newton.
00:33:32But if it is two times, then which one will be more anymore?
00:33:37Then the middle value will be equal to 1 to 12.
00:33:40theta by 2, theta by 2.
00:33:54a vector
00:34:39by
00:35:052, theta by 2.
00:35:54a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:36:22a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:36:48a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:37:15a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:37:42a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:38:09a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:38:36a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:39:04a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:39:33a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:40:03a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:40:33a vector by 2, theta by 2, theta by 2, theta by 2, theta by 2.
00:41:03a vector by 2, theta by 2, theta by 2, theta by 2.
00:41:33a vector by 2, theta by 2, theta by 2, theta by 2.
00:42:03a vector by 2, theta by 2, theta by 2, theta by 2.
00:42:33a vector by 2, theta by 2, theta by 2, theta by 2.
00:43:03a vector by 2, theta by 2, theta by 2, theta by 2.
00:43:32a vector by 2, theta by 2, theta by 2, theta by 2.
00:44:02a vector by 2, theta by 2, theta by 2.
00:44:32a vector by 2, theta by 2, theta by 2.
00:45:02a vector by 2, theta by 2, theta by 2.
00:45:32a vector by 2, theta by 2, theta by 2.
00:46:02a vector by 2, theta by 2, theta by 2.
00:46:32a vector by 2, theta by 2, theta by 2.
00:47:00a vector by 2, theta by 2, theta by 2.
00:47:28a vector by 2, theta by 2, theta by 2.
00:47:56a vector by 2, theta by 2, theta by 2.
00:48:24a vector by 2, theta by 2, theta by 2.
00:48:51a vector by 2, theta by 2, theta by 2.
00:49:21a vector by 2, theta by 2, theta by 2.
00:49:51a vector by 2, theta by 2, theta by 2.
00:50:21a vector by 2, theta by 2, theta by 2.
00:50:51a vector by 2, theta by 2, theta by 2.
00:51:21a vector by 2, theta by 2, theta by 2.
00:51:51a vector by 2, theta by 2, theta by 2.
00:52:21a vector by 2, theta by 2, theta by 2.
00:52:51a vector by 2, theta by 2, theta by 2.
00:53:21a vector by 2, theta by 2, theta by 2.
00:53:51a vector by 2, theta by 2, theta by 2.
00:54:19a vector by 2, theta by 2, theta by 2.
00:54:47a vector by 2, theta by 2, theta by 2.
00:55:15a vector by 2, theta by 2, theta by 2.
00:55:43a vector by 2, theta by 2, theta by 2.
00:56:11a vector by 2, theta by 2, theta by 2.
00:56:38a vector by 2, theta by 2, theta by 2.
00:57:06a vector by 2, theta by 2, theta by 2.
00:57:36a vector by 2, theta by 2, theta by 2.
00:58:06a vector by 2, theta by 2, theta by 2.
00:58:36a vector by 2, theta by 2, theta by 2.
00:59:06a vector by 2, theta by 2, theta by 2.
00:59:36a vector by 2, theta by 2, theta by 2.
01:00:06a vector by 2, theta by 2, theta by 2.
01:00:36a vector by 2, theta by 2, theta by 2.
01:01:06a vector by 2, theta by 2, theta by 2.
01:01:36a vector by 2, theta by 2, theta by 2.
01:02:06a vector by 2, theta by 2, theta by 2.
01:02:36a vector by 2, theta by 2, theta by 2.
01:03:06a vector by 2, theta by 2, theta by 2.
01:03:34a vector by 2, theta by 2, theta by 2.
01:04:02a vector by 2, theta by 2, theta by 2.
01:04:29a vector by 2, theta by 2, theta by 2.
01:04:57a vector by 2, theta by 2, theta by 2.
01:05:27a vector by 2, theta by 2, theta by 2.
01:05:57a vector by 2, theta by 2, theta by 2.
01:06:27a vector by 2, theta by 2, theta by 2.
01:06:57a vector by 2, theta by 2, theta by 2.
01:07:27a vector by 2, theta by 2, theta by 2.
01:07:57a vector by 2, theta by 2, theta by 2.
01:08:27a vector by 2, theta by 2, theta by 2.
01:08:57a vector by 2, theta by 2, theta by 2.
01:09:27a vector by 2, theta by 2, theta by 2.
01:09:57a vector by 2, theta by 2, theta by 2.
01:10:27a vector by 2, theta by 2, theta by 2.
01:10:57a vector by 2, theta by 2, theta by 2.
01:11:27a vector by 2, theta by 2, theta by 2.
01:11:57a vector by 2, theta by 2, theta by 2.
01:12:25a vector by 2, theta by 2, theta by 2.
01:12:55a vector by 2, theta by 2, theta by 2.
01:13:25a vector by 2, theta by 2, theta by 2.
01:13:54a vector by 2, theta by 2, theta by 2.
01:14:24a vector by 2, theta by 2, theta by 2.
01:14:54a vector by 2, theta by 2, theta by 2.
01:15:24a vector by 2, theta by 2, theta by 2.
01:15:54a vector by 2, theta by 2, theta by 2.
01:16:24a vector by 2, theta by 2, theta by 2.
01:16:54a vector by 2, theta by 2, theta by 2.
01:17:24a vector by 2, theta by 2, theta by 2.
01:17:54a vector by 2, theta by 2, theta by 2.
01:18:24a vector by 2, theta by 2, theta by 2.
01:18:52a vector by 2, theta by 2, theta by 2.
01:19:22a vector by 2, theta by 2, theta by 2.
01:19:52a vector by 2, theta by 2, theta by 2.
01:20:22a vector by 2, theta by 2, theta by 2.
01:20:52a vector by 2, theta by 2, theta by 2.
01:21:22a vector by 2, theta by 2, theta by 2.
01:21:52a vector by 2, theta by 2, theta by 2.
01:22:22a vector by 2, theta by 2, theta by 2.
01:22:52a vector by 2, theta by 2, theta by 2.
01:23:22a vector by 2, theta by 2, theta by 2.
01:23:52a vector by 2, theta by 2, theta by 2.
01:24:22a vector by 2, theta by 2, theta by 2.
01:24:52a vector by 2, theta by 2, theta by 2.
01:25:22a vector by 2, theta by 2, theta by 2.
01:25:52a vector by 2, theta by 2, theta by 2.
01:26:22a vector by 2, theta by 2, theta by 2.
01:26:52a vector by 2, theta by 2, theta by 2.
01:27:22a vector by 2, theta by 2, theta by 2.
01:27:52a vector by 2, theta by 2, theta by 2.
01:28:22a vector by 2, theta by 2, theta by 2.
01:28:52a vector by 2, theta by 2, theta by 2.
01:29:22a vector by 2, theta by 2, theta by 2.
01:29:52a vector by 2, theta by 2, theta by 2.
01:30:22a vector by 2, theta by 2, theta by 2.
01:30:52a vector by 2, theta by 2, theta by 2.
01:31:22a vector by 2, theta by 2, theta by 2.
01:31:52a vector by 2, theta by 2, theta by 2.
01:32:22a vector by 2, theta by 2, theta by 2.
01:32:52a vector by 2, theta by 2, theta by 2.
01:33:22a vector by 2, theta by 2, theta by 2.
01:33:52a vector by 2, theta by 2, theta by 2.
01:34:22a vector by 2, theta by 2, theta by 2.
01:34:52a vector by 2, theta by 2, theta by 2.
01:35:22a vector by 2, theta by 2, theta by 2.
01:35:52a vector by 2, theta by 2, theta by 2.
01:36:22a vector by 2, theta by 2, theta by 2.
01:36:52a vector by 2, theta by 2, theta by 2.
01:37:22a vector by 2, theta by 2, theta by 2.
01:37:52a vector by 2, theta by 2, theta by 2.
01:38:20a vector by 2, theta by 2, theta by 2.
01:38:48a vector by 2, theta by 2, theta by 2.
01:39:18a vector by 2, theta by 2, theta by 2.
01:39:48a vector by 2, theta by 2, theta by 2.
01:40:18a vector by 2, theta by 2, theta by 2.
01:40:48a vector by 2, theta by 2, theta by 2.
01:41:18a vector by 2, theta by 2, theta by 2.
01:41:48a vector by 2, theta by 2, theta by 2.
01:42:02a vector by 2, theta by 2, theta by 2.
01:42:32a vector by 2, theta by 2, theta by 2.
01:43:02a vector by 2, theta by 2, theta by 2.
01:43:32a vector by 2, theta by 2, theta by 2.
01:44:02a vector by 2, theta by 2, theta by 2.
01:44:32a vector by 2, theta by 2, theta by 2.