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Vector Analysis

  1. Sep 20, 2012 #1

    dpa

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    1. The problem statement, all variables and given/known data

    Let x,y is in Vn, such that x is not equal to zero.
    Show that you can find vectors y and y// is in Vn such that y=y + y// and y// is parallel to x and y is perpendicular to x.

    2. Relevant equations
    x//y => x=ky
    x.y=0 if x┴y

    3. The attempt at a solution
    I calculated the components of y along y and y// and showed that the synthesis of these gives y. I was adviced to use x as well. So I need different method.

    By supposing y//=kx,
    y=y-y//
    we write,
    kx.(y-y//)=0
    and I was asked to find k and show,y=y + y//. I have no idea how to proceed after the above line.

    Thank You
     
  2. jcsd
  3. Sep 20, 2012 #2

    jbunniii

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    Do you know how to project a vector onto another vector?
     
  4. Sep 20, 2012 #3

    dpa

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    I was suggested not to use vector projections that are in trigonometric forms.
    As for the y||=(x.y/x^2).x form,
    I know that what I can do is find
    y||=(y.kx/(kx)^2).kx [sorry, k is not bold here]
    and yperp.=y-xk.,
    I have no idea hence forth.
     
  5. Sep 20, 2012 #4

    jbunniii

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    This is what I meant by vector projection. In fact, you can take k = (x.y/x^2), can't you?
     
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