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Question

Prove that for any three vectors a,b and c, [(a+b) (b+c) (c+a)]=2[a b c].

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Solution

LHS: [(a+b)( b+c) (c+a)]
=(a+b).[b+c×c+a]
=(a+b).[b×c+b×a+c×c+c×a]
=a.(b×c)+b.(c×a)
=[a b c]+[b c a]
2[a b c]= RHS
Hence proved.

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