The square of resultant of two equal forces is three times their product. Angle between the force is

Options

A. `pi`
B. `pi/2`
C. `pi/4`
D. `pi/3`

Answer

D

Explanation

Let be the angle between vectors `lt b gt P lt //b gt ` and `lt b gt B lt//b gt`
Whose resultant is `lt b gt R lt //b gt`
Hence,`P = Q` and `R^2 = 3PQ = 3P^2`
As `R^2 = P^2 + Q^2 + 2PQ cos theta`
or `3P^2 - 2P^2 = 2P^2 cos theta`
or `P^2 = 2P^2 cos theta`
or `1 = 2 cos theta`
`therefore cos theta = 1/2 ,` thus , `cos theta = cos 60^@`
or `theta = 60^@ = pi/3`