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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 acute angle between the vectors b and c, then sinθ equals

A
223
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B
23
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C
23
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D
13
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Solution

The correct option is B 223
Given, (a×b)×c=13|b||c|a

Using the vector triple cross product we have

(ac)b(bc)a=13|b||c|a

Equating the coefficient of a, we get

|b||c|cosθ=13|b||c|cosθ=13

sinθ=1cos2θ=119=223

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