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Question

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

A
23
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B
233
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C
223
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D
23
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Solution

The correct option is B 223
(a×b)×c=c×(c×b)=[(c.b)a(c.a)b]=(c.a)b(c.b)a13b|c||a|(c.b)=13b|c||c|bcosθ=13b|c|cosθ=13sinθ=223Hence,optionCiscorrectanswer.

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