Question

The magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector. What is the angle between the two vectors?

Answer 1

Given:
$|\overrightarrow{A}|=|\overrightarrow{B}|=|\overrightarrow{R}|$

The resultant of two vectors is given by

$R^2=A^2+B^2+2AB\cos \theta ........\left(1\right)$

It is given that $R=A=B$

Putting these values in eqn. $\left(1\right)$, we have

$A^2=A^2+A^2+2A^2\cos \theta$

$\Rightarrow \cos \theta =-\frac{1}{2}$

$\therefore \theta ={120}^{\circ }$

Hence, the correct choice is $\left(\text{C}\right)$.