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Thread: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is equal

  1. #1
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    Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is equal

    Hi There

    I'm really struggling with these question:

    Projau = Projav is true for some vectors a, u and w.

    Show: u v = v a
    Show: counter example to show that u isnt equal to v

    I seem to have these looooooooong roundabout routes that arent making sense for the first, and for the second i have no idea how to work out a counter example!

    Any help would be very appreciated!
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  2. #2
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    Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

    Quote Originally Posted by LucyA View Post
    Hi There

    I'm really struggling with these question:

    Projau = Projav is true for some vectors a, u and w.

    Show: u v = v a
    Show: counter example to show that u isnt equal to v !
    Please review and/or correct your post.
    Don't you mean $\large{\vec{u}\cdot\vec{a}=\vec{v}\cdot\vec{a}~?} $
    Can we assume that $\text{Proj}_{\vec{a}}\vec{u}=\dfrac{\vec{u}\cdot \vec{a}}{\vec{a}\cdot \vec{a}}\vec{a}~?$
    Thanks from topsquark
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    Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

    thats the problem im having! but no, definitely that??? thanks so much for replying!
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    Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

    oh gosh sorry just got informed there was an error there! however, for the second question, i have no idea how to go about counter example????
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    Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

    Quote Originally Posted by LucyA View Post
    oh gosh sorry just got informed there was an error there! however, for the second question, i have no idea how to go about counter example????
    Consider the vectors: $\vec{a}=<1 ,1 ,0 >,~\vec{u}<1 ,1 ,\sqrt{2} >,~\&~\vec{v}<1,1,-\sqrt{2} >$
    Thanks from topsquark and LucyA
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  6. #6
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    Re: Projection Thereom- When Proja Is equal for 2 Vectors, Prove the Dot Product is e

    woo!
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