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Previous Year Question (PYQs)



If $\hat n_1,\hat n_2$ are two unit vectors and $\theta$ is the angle between them, then $\cos\dfrac{\theta}{2}$ is equal to





Solution

$|\hat n_1+\hat n_2|^2=2(1+\cos\theta)$

So,
$|\hat n_1+\hat n_2|=2\cos\dfrac{\theta}{2}$

Hence,
$\cos\dfrac{\theta}{2}=\dfrac12|\hat n_1+\hat n_2|$


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