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Question

If a,b and care unit vectors such thatax(bxc)=12b, then the angle between aand c is?


A

π/6

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B

π/4

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C

π/2

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D

π/3

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Solution

The correct option is D

π/3


Find the angle between aand c:

Given that a,b and care unit vectors such thatax(bxc)=12b

(a.c)b(a.b)c=12b

If we compare both the sides,

a.c=1/2

The angle between aand c is given by

cosθ=(a.c)|a||c|cosθ=121×1[sinceaandcareunitvectors|a|=1,|c|=1]cosθ=12cosθ=cos(π/3)

Therefore, θ=π/3

Hence, the correct option is D.


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