Question

Find the magnitude of each of the two vectors of $\overrightarrow{a}$ and $\overrightarrow{b}$, having same magnitude such that the angle between them is ${60}^{\circ }$ and their scalar product is $\frac{9}{2}$.

Answer 1

As $\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|cos\theta \Rightarrow \frac{9}{2}=|\overrightarrow{a}||\overrightarrow{a}|cos{60}^{\circ }\Rightarrow \frac{9}{2}=|\overrightarrow{a}{|}^2\times \frac{1}{2}\therefore |\overrightarrow{a}|=3$. Hence $|\overrightarrow{a}|=|\overrightarrow{b}|=3$.