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Question

If a and b are unit vectors and θ is the angle between them, then show that |ab|=2sinθ2.

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Solution

a.b=|a||b|cosθ
=1.1.cosθ
=cosθ
Now,
|ab|=(ab)2
=|a|2+|b|22a.b
=1+12cosθ
=2(1cosθ)
|ab|2=2.2sin2θ2
|ab|=2sinθ2

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