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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It looks good to me though a little more complicated than necessary.
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] so that reduces to .
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