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Question

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

A
a.b=b.c=0
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B
b.c=c.a=0
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C
c.a=a.b=0
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D
a.b=b.c=c.a=0
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Solution

The correct option is C a.b=b.c=c.a=0
If θ is the angle between a and band
ϕ is the angle between a×b and c, then (a×b).c=abcsinθcosϕ
sinθ=1,cosϕ=1
θ=π2,ϕ=0
ab,c is along a×b
ca,cb
a.b=b.c=c.a=0

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