Question

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 :

• A. $\sin^{-1} \left[\frac{n^{2}-1}{n^{2}+1}\right]$
• B. $\cos^{-1} \left[\frac{n -1}{n+1}\right]$
• C. $\cos^{-1} \left[\frac{n^{2}-1}{n^{2}+1}\right]$
• D. $\sin^{-1} \left[\frac{n -1}{n+1}\right]$

Answer 1

Answer: (C)

$\cos^{-1} \left[\frac{n^{2}-1}{n^{2}+1}\right]$

Answer 2

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