Question

Two equal forces have square of their resultant equal to three times their product. Find the angle between them.

Answer 1

Let forces be F, F
resultant$=\sqrt{F^2+F^2+2F^2\cos \theta }$
$product=F^2$
$2F^2+2F^2{\cos }^2\theta =3F^2$
$2F^2{\cos }^2\theta =F^2$
${\cos }^2\theta =\frac{1}{2}$
${\cos }^2\theta =\frac{1}{\sqrt{2}}$ $\theta ={45}^{\circ }$