Q. Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. The magnitude of $(\vec{A} + \vec{B})$ is 'n' times the magnitude of $(\vec{A} - \vec{B})$ . The angle between $\vec{A}$ and $\vec{B}$ is :

Solution:

$\left|\vec{A} + \vec{B}\right| = 2a \cos\theta /2$ .....(1)
$ \left|\vec{A} -\vec{B}\right| = 2 a \cos \frac{\left(\pi-\theta\right)}{2} = 2a \sin\theta/2 $ ......(2)
$ \Rightarrow n\left(2a \cos \frac{\theta}{2}\right)=2a \frac{\sin\theta}{2} $
$ \Rightarrow \tan \frac{\theta}{2} =n $

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