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Show that it is orthogonal to both u and v

  1. Sep 11, 2009 #1


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    find u X v and show that it is orthogonal to both u and v.

    u= 6k
    v=-i + 3j + k


    This is what I got from the picture, but my teacher said that I have one more step to do to show that they are orthogonal, I need to do uxv

    uxw = (0*-18)+(0*-6)+(6*0)= ?

    and also vxw=?

    If both are zero, the vectors are orthogonal.

    But my problem is I don't know how to find w. Can any one please explain it to me? Thank you very much!
  2. jcsd
  3. Sep 11, 2009 #2


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    uxw is a vector. Where are your i, j, k? I think you have it correct on your paper.

    If you want to show uxw is orthogonal to u and v, remember that two nonzero vectors are orthogonal if their dot product is 0.
  4. Sep 12, 2009 #3
    Call the orthogonal vector w.

    If two vectors are orthogonal then the angle between them is 900

    You can prove it using the dot product:

    [tex]\mathbf{u} \cdot \mathbf{w} = 0[/tex]


    [tex]\mathbf{v} \cdot \mathbf{w} = 0[/tex]

    or finding cos(u,w) and cos(v,w) for the cross product (since you already find w). :smile:
  5. Sep 12, 2009 #4


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    Excuse me, but you first say "find u X v and show that it is orthogonal to both u and v" but then start talking about "u x w" and "v x w". Where did "w" come from? If you mean that w= u x v, then, as njama said, you want to look at the dot product of w with u and v, not the cross product. You do NOT, by the way, need to divide by ||u x v|| since the problem says nothing about a unit vector.
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