Question

Two forces each of $10N$ act at an angle ${60}^o$ with each other. The magnitude & direction of the resultant with respect to one of the vectors is

Answer 1

From the formula $\left|\overrightarrow{C}\right|=\sqrt{A^2+B^2+2AB\cos \theta }=\sqrt{100+100+2\times 10\times 10\times \frac{1}{2}}=\sqrt{300}$

Magnitude $=10\sqrt{3}$

Direction :

$\angle \varphi ={tan}^{-1}\left(\frac{B\sin \theta }{A+B\cos \theta }\right)={tan}^{-1}\left(\frac{10\times \frac{\sqrt{3}}{2}}{10+10\times \frac{1}{2}}\right)={tan}^{-1}\left(\frac{5\sqrt{3}}{15}\right)={tan}^{-1}\left(\frac{\sqrt{3}}{3}\right)$