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Question

For non-zero vectors a,b,c;(a×b)c=abc holds if and only if

A
ab=0,bc=0
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B
bc=0,ca=0
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C
ca=0,ab=0
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D
ab=bc=ca=0
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Solution

The correct option is C ab=bc=ca=0
We have (a×b)c=abc
absinθ^nc=abc
abcsinθcosα=abc
|sinθ||cosα|=1
θ=π2 and α=0
ab and c is parallel to ^n
ab and c to both a and b
a, b, c are mutually perpendicular
ab=bc=ca=0
Hence (D) is correct.

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