If a=vector OA, b=vector OB and c=vector OC where points A, B and C are non-collinear, show that the vector v=(a x b) + (b x c) + (c x a) is perpendicular to the plane that contains A, B and C.
by 
emma3001
ANSWERS: 1
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AB is in the plane. So is BC so b-a and c-b are in the plane. So (b-a) x (c-b) is normal to the plane. = bxc - axc -bxb + axb = bxc - axc + axb (bxb is zero) = axb + bxc - axc = axb + bxc + cxa It almost does itself.
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