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Question

If a, b, c are non-coplanar vectors, then a · b ×c c ×a ·b +b · a ×c c · a ×b is equal to
(a) 0
(b) 2
(c) 1
(d) none of these

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Solution

(a) 0

We havea.b×cc×a.b +b.a×cc.a×b=abccab + baccab By definition of scalar tiple product=abcabc +-abcabc Change in cyclic order of vectors changes the sign of the scalar triple product=1-1=0

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