Question

The magnitude of resultant of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ of equal magnitude is also same as that of the magnitude of individual vectors. The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

• A. $\pi /4$
• B. $\pi /3$
• C. $\pi /2$
• D. $\left(2/3\right)\pi$

Answer 1

The correct option is D $\left(2/3\right)\pi$

Let $\overrightarrow{R}$ be resultant and $\theta$ angle between $\overrightarrow{A}\&\overrightarrow{B}$.
Given: $\left|\overrightarrow{R}\right|=\left|\overrightarrow{A}\right|=\left|\overrightarrow{B}\right|=a$
$R^2=A^2+B^2+2AB\cos \theta$
$a^2=a^2+a^2+2a^2\cos \theta$

$\cos \theta =\frac{-1}{2}or\theta =\frac{2\pi }{3}$