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Question

For non-zero vectors a,b,c; |(a×b).c|=|a||b||c| holds if

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

The correct option is D a.b=b.c=c.a=0
We have
(a×b).c=|c|a×bcosϕ
=|c||a|bsinθcosϕ
(where ϕ is angle between a+b & c
θ is angle between a & b)
sinθ=1 ωϕ=1
θ=π2 ϕ=0
So ab c||a×b
So a.b=c.a=c.b=0

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