# What is the angle between two forces of equal magnitude, F_a and F_b, when the magnitude of their resultant is also equal to the magnitude of either of these forces?

Jul 28, 2016

$\theta = \frac{2 \pi}{3}$

#### Explanation:

Let the angle between ${F}_{a} \mathmr{and} {F}_{b}$ be $\theta$ and their resultant is ${F}_{r}$ So

${F}_{r}^{2} = {F}_{a}^{2} + {F}_{b}^{2} + 2 {F}_{a} {F}_{b} \cos \theta$
Now by the given condition
let ${F}_{a} = {F}_{b} = {F}_{r} = F$

So

${F}^{2} = {F}^{2} + {F}^{2} + 2 {F}^{2} \cos \theta$

$\implies \cos \theta = - \frac{1}{2} = \cos \left(2 \frac{\pi}{3}\right)$

$\therefore \theta = \frac{2 \pi}{3}$