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Question

Let a,b and c be non-zero vectors such that no two are collinear and (a×b)×c=(13)|b||c|a. If θ is the angle between the vectors b and c, then the value of sin θ is

A
13
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B
223
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C
23
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D
223
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Solution

The correct option is D 223
We have 13|b||c|a=(a×b)×c
We know that (a×b)×c=(ac)b(bc)a 13|b||c|a=(ac)b(bc)a
on comparing both sides, we get
bc=13|b||c|
cosθ=13sinθ=223

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