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Near the end, the author claims that if a,b,c form a basis of R3,
then the cross products a x b, b x c, and c x a are orthogonal. This is false. E.g., a=(1,1,0), b=(0,1,1), c=(1,0,1) implies a x b = (+1,-1,+1), b x c = (+1,+1,-1), c x a = (-1,+1,+1). However, this "dual basis" still serves its claimed purpose,
which essentially is to precompute part of Cramer's rule. |