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Question

If θ is the angle between unit vectors a and b, then sin[θ2] equals

A
12|a+b|
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B
12|a×b|
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C
121(a.b)
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D
12|ab|
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Solution

The correct option is A 12|a+b|
Solution - According to the question a and b are two unit vectors. |a|=|b|=1|ab|2=(ab)(a+b)=|a|2+|b|22(|a||b|cosθ)=1+12cosθ=22cosθ

We know that,
1cosθ=2sin2θ2 |ab|2=2×2sin2θ2 sinθ2=12|ab|

Hence ,(A) is the correct option.

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