Defining the angle between vectors | Vectors and spaces | Linear Algebra | Khan Academy

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  • เผยแพร่เมื่อ 11 ธ.ค. 2024

ความคิดเห็น • 69

  • @AlejandroVidalesAller
    @AlejandroVidalesAller 10 ปีที่แล้ว +27

    This is the video that shows me how from the law of cosines, I get the formula for the angle between two vectors. Thank you!!

  • @ratnakarbachu2954
    @ratnakarbachu2954 3 ปีที่แล้ว +2

    Really these videos are more useful to learn linear algebra from basics.I appreciate for help.
    Indeed , i struggled a lot to learn LA from various sources, but here you made very simple and clear.
    thanks to god and you guys.

  • @AdeptusTacticus
    @AdeptusTacticus 9 ปีที่แล้ว +18

    KHAAAAAAAAANNNNNNNNNNNNNN!!!!!!

    • @slap_my_hand
      @slap_my_hand 7 ปีที่แล้ว +1

      Exactly what i thought when i saw the title

  • @flatwall4569
    @flatwall4569 ปีที่แล้ว +1

    Defining an angle starts @9:50

  • @risingabove5108
    @risingabove5108 11 ปีที่แล้ว +10

    I wish you did an example problem on this...

  • @petercope6666
    @petercope6666 4 ปีที่แล้ว +2

    Humble brag: this won't be earth shattering, but it kind of is

  • @Ferrus91
    @Ferrus91 15 ปีที่แล้ว

    Excellent, I am so glad these videos actually prove results rather than churn out computations.

  • @norwayte
    @norwayte 15 ปีที่แล้ว +2

    Enlightening. Brilliant. Good. And a distinction as bonus. Thank you.

  • @Sothatjusticecanbedone
    @Sothatjusticecanbedone 5 ปีที่แล้ว +1

    this is a very important concept of angle for infinite many dimension

  • @cgsrtkzsytriul
    @cgsrtkzsytriul 12 ปีที่แล้ว +1

    theta = arcos ( (vector A dot product vector B) / (magnitude A * magnitude B) )

  • @VexingCode
    @VexingCode 13 ปีที่แล้ว

    Love your videos Sal, please come to my University and teach Physics, math and everything lol

  • @LAnonHubbard
    @LAnonHubbard 14 ปีที่แล้ว +1

    Great refresher for me, thanks.

  • @GreyWatcher
    @GreyWatcher 15 ปีที่แล้ว

    I am quite aware of several mathematicians who where Muslims. They produced several great contributions to mathematics. My point was simply that our digits has nothing to do with Islam.
    The Wikipedia entry of "Mathematics in medieval Islam" is a good place to look for a small sample of those contributions.

  • @Kisongochi
    @Kisongochi 2 ปีที่แล้ว +1

    What a lesson

  • @devjha5223
    @devjha5223 6 ปีที่แล้ว +6

    “Run of the mill triangle”

  • @afroze4all
    @afroze4all 13 ปีที่แล้ว

    @greyman000 U R right....numbers which we call arabic are not actually arabic they are first used by Indians who introduced them....I am Indian and I am proud of it......now coming to Islam.....In Quran you can see many scientific fact which are now recently discovered......so Its true religion and I am proud to be a Muslim....

    • @georgekhalil2779
      @georgekhalil2779 5 ปีที่แล้ว

      But your excluding Arabs who created a lot of the fundamental or Isaac Newton who created calculus why can’t we just say people are great. Seriously religion has nothing to do with math.

  • @chychychyp
    @chychychyp 10 หลายเดือนก่อน

    11:30 어쩌면 내적의 탄생과 관련된

  • @vrushabh1010
    @vrushabh1010 3 ปีที่แล้ว

    Thank you.

  • @yashpatil1309
    @yashpatil1309 7 ปีที่แล้ว

    thank you so much for this video khan Academy!!!

  • @sezerozer382
    @sezerozer382 10 ปีที่แล้ว

    your expression style is relaxing my mind :)

  • @jameswilkinson8060
    @jameswilkinson8060 6 ปีที่แล้ว

    18:53 so its perpendicular then? love the way he says it too

  • @You2ubeGuy01
    @You2ubeGuy01 12 ปีที่แล้ว

    Wow, a very eye opening video.

  • @kuldude12222
    @kuldude12222 12 ปีที่แล้ว

    Although you are right don't deny the fact that Muslims did contribute quite a lot to what mathematics is today. The use of algebra in geometry is just one example of many.

  • @HPRCMax
    @HPRCMax 13 ปีที่แล้ว

    i like the way he pronounces the word "perpendicular"

  • @theowlsgo
    @theowlsgo 14 ปีที่แล้ว

    @regingwapo he states the zero vector is orthogonal to everything else at 23:50

  • @eileenBrain
    @eileenBrain 12 ปีที่แล้ว

    what i ment was there was no example of this formula at work. Anyway i was a newb at linear algebra back then.

  • @saun_sa
    @saun_sa 4 ปีที่แล้ว

    sal khan is like smarty shroud

  • @GreyWatcher
    @GreyWatcher 15 ปีที่แล้ว

    Our digits (0, 1, ..., 9) are called "arabic numbers", but they have nothing to do with Islam. First, they where used by the arabic people before Muhammed, and second the arabs accually adopted them from India.
    The only reason they are called arabic numbers are because the europeans first learned about them from the arabs, roughly at the time of the crusades. Before that the europeans had used the roman numbers, which are quite clumsy in mathematics.

  • @mintoo2cool
    @mintoo2cool 12 ปีที่แล้ว

    orthogonal applies to higher dimensions whereas perpendicular applies to lines only. At least that is how I think of The difference between the two.

  • @theshwinkie
    @theshwinkie 11 ปีที่แล้ว

    I really hope that is your real name because that would be badass

  • @jasonlaboy
    @jasonlaboy 8 ปีที่แล้ว

    What do you do if the magnitude of both is the same ?

  • @rashikahmed9372
    @rashikahmed9372 7 ปีที่แล้ว

    Make a video about parallel vectors.

    • @syedrayyanshah-lo1kr
      @syedrayyanshah-lo1kr 6 หลายเดือนก่อน

      brother im so confused if two vectors have same magnitude and opposite direction we call it antiparallel in physics but our maths sir states that they are not anti parallel they are still parallel and i dont know where to get the correct ans of it or explanation

  • @MrPankaj102
    @MrPankaj102 11 ปีที่แล้ว

    angle between (A+B) and (A cross B) sir plz ans this??

  • @dannykhondiwa9218
    @dannykhondiwa9218 7 ปีที่แล้ว

    if the magnitude of vector a is 4 and vector c is 2 and the angle between vector a and b is 60 degrees while d=4a minus c find the magnitude of d. is this question solvable?

  • @shashibhushansharma1383
    @shashibhushansharma1383 7 ปีที่แล้ว

    thank you sir for this lecture. you are telling that 'zero vector is orthogonal to everything' why even dot product only valid for non zero vector?

    • @rayniac211
      @rayniac211 4 ปีที่แล้ว

      Dot product is defined for all vectors of same dimensions, even for zero vectors. It is the angle that is undefined if one vector is a zero vector.

  • @regingwapo
    @regingwapo 14 ปีที่แล้ว

    sal, my linear algebra book defines the zero vector to be perpendicular to every vector. Yet you said that for a and b to be perpendicular, both of them must be non zero.
    help!!

  • @GreyWatcher
    @GreyWatcher 15 ปีที่แล้ว

    What on earth gave you the impression that I ever thought anything different?
    I have studied Islam, as well as the other world religions. I know that Islam as a religion is quite friendly with science, despite what some creationists (like this guy: /watch?v=L9R0XI2G3s4 ) seam to think.
    I simply pointed out a very common misunderstanding about the Arabic numbers.

    • @georgekhalil2779
      @georgekhalil2779 5 ปีที่แล้ว

      Grey Watcher also it depends on the country my mother is from Egypt and for a while they were barred from studying biology and especially anatomy.

    • @muhammadashshiddieqi8653
      @muhammadashshiddieqi8653 2 ปีที่แล้ว +1

      ĹBBBŞČ MÅÝ F W Ù ÑĒĒĐ ĒŞP ČÒÙŘŞĒŞ Ñ ĶÀHVÈÌÑ ČÒFƏĔŞHÒP Ñ MZ.ŞHÌDĐÌĒQÌ ÇHÈÇĶÌŤ

  • @debendragurung3033
    @debendragurung3033 8 ปีที่แล้ว

    oh boy, how long will it take for me to start learning Topology, assuming I just half understood this. If its two years at least... I am going to find a proper job

  • @spncrgrn
    @spncrgrn 14 ปีที่แล้ว

    Between vectors... between vectors... betweeeeeeen... vectors...
    Hahaha, I'm just kidding, great job

  • @GreyWatcher
    @GreyWatcher 12 ปีที่แล้ว

    @kuldude12222 Why do you think I'm denying that?

  • @Blossoms777
    @Blossoms777 12 ปีที่แล้ว +8

    Because God created the Universe, planned out its structure, chemistry, layout, and all of the infinite as well as finite things within it. All this stuff works together, and that alone proves God's existence, and Omnipotence. The Universe and all of its complexities, formulas, and intricate workings was thought up in the mind of God and made into physical reality. The Universe is awesome, and God is awesome!!

    • @georgekhalil2779
      @georgekhalil2779 5 ปีที่แล้ว +3

      Lol what ? First it was people who created math. Second why are you preaching at a math video.

    • @jonathancurtis5122
      @jonathancurtis5122 5 ปีที่แล้ว +1

      Well said.

    • @盧嘉浠
      @盧嘉浠 2 ปีที่แล้ว +2

      @@georgekhalil2779 If you have studied enough math, you should know th mathematics is discovered by human, not created.

    • @DavidMindfulThoughts
      @DavidMindfulThoughts ปีที่แล้ว

      Guys Listen, every part of knowledge in this world comes from GOD himself, it is not about preaching man, it's a natural thing that's it

  • @fashionvella730
    @fashionvella730 ปีที่แล้ว

    Hi Sal why not you make a video that what is the method of you for learning math why not you teach us how to catch ha fish instead of you catch for us

  • @tsiebring477
    @tsiebring477 11 ปีที่แล้ว

    I really like your channel, and I think it is very useful, but could you please try to repeat your words a bit less?
    example:
    "of an angle, of an angle between vectors, between vectors, between vectors" (00:36)

    • @lachlan_bakewell
      @lachlan_bakewell 10 ปีที่แล้ว +15

      Repetition of terms is an effective teaching method. It is also one of the many great things that sets Khan out from the rest.

    • @herpderp818
      @herpderp818 10 ปีที่แล้ว +6

      Since he is teaching and talking as he writes, I think it's hard to make sure he's writing the correct thing whilst he says something else, and he then has to repeat himself. If not he may end up writing what he's saying, not what he meant to write.

  • @afroze4all
    @afroze4all 13 ปีที่แล้ว

    @Osman9100 Hi bro....little correction but dont think me as non-muslims I am a muslim and I am from India.....one thing I can say for sure Math, science, medicine, astronomy and many other sciences were first invented by Indians in the world not by any Arabs or European even. Coming to Islam I will say the only true religion on the phase of earth as it explains us about such great mysterious of time which were not of human knowledge, and this is not by arabs this is by almight god Allah.....

  • @kenmeyer100
    @kenmeyer100 5 ปีที่แล้ว

    I don't understand the motivation for the proof he is giving in the first part of the video (using the triangle inequality theorem). If I construct a triangle using three vectors, then by definition they are going to satisfy the conditions he is giving the proof for.

    • @rayniac211
      @rayniac211 4 ปีที่แล้ว

      "If I construct... "
      But can you? That is what Sal wants to verify before he moves on with the rest of the proof.

  • @skyfaze
    @skyfaze 14 ปีที่แล้ว

    why so much beef =/

  • @hussein688
    @hussein688 14 ปีที่แล้ว

    how did religion get into this???? stick to the topic for once guys.. btw great work Sal.

  • @pithikoulis
    @pithikoulis 13 ปีที่แล้ว

    @afroze4all What has any god to do with math? As you said math was invented by people. Why mix religion in everything when it's fine on its own?

  • @mikkelgedehansen9479
    @mikkelgedehansen9479 4 ปีที่แล้ว

    This way of explaining the concept is completely useless to anyone with a visualizing mind...-A shame since all the previous vector sections have been great.

  • @eileenBrain
    @eileenBrain 13 ปีที่แล้ว

    Ok, so he mentions that "(a . b) = ||a|| ||b|| cos" can be used to find the angle between two vectors but then fails to show how. This videos are starting to suck more and more... NICE WORK SALL!!

  • @Troynjk
    @Troynjk 15 ปีที่แล้ว

    the quality of the video is bad

  • @ElectronicMuic
    @ElectronicMuic 4 ปีที่แล้ว

    the linear algebra video all long, lost my focus there, and there`s less interactive practice in that course, im guessing its because this video is from 2009

  • @hussein688
    @hussein688 14 ปีที่แล้ว

    how did religion get into this???? stick to the topic for once guys.. btw great work Sal.