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Thread: Vector product

  1. #1
    Senior Member
    Oct 2009

    Vector product

    I think I have done this question but is there a better way? Prove that if the numbers p, q, r and s satisfy ps=qr, then (pa+qb) x (ra+sb) = 0. a and b are vectors.
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  2. #2
    MHF Contributor

    Apr 2005

    Re: Vector product

    It looks good to me though a little more complicated than necessary.

    (pa+ qb)\times(ra+ sb)= pa\times ra+ pa\times sb+ qb\times ra+ qb\times sb
    Of course, you can take out the numbers: pr(a\times a)+ ps(a\times b)+ qr(b\times a)+ qs(b\times b)[tex]
    a\times a= b\times b= 0 so that reduces to ps(a\times b)+ ar(b\times a)= ps(a\times b)- qr(a\times b)= (ps- qr)(a\times b).
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