Question

Resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is inclined at ${45}^{\circ }$ to either of them. What is the magnitude of the resultant?

• A. $\sqrt{P^2+Q^2}$
• B. $\sqrt{P^2-Q^2}$
• C. $P+Q$
• D. $P-Q$

Answer 1

The correct option is A $\sqrt{P^2+Q^2}$

Let resultant of the two vectors be $\overrightarrow{R}=\overrightarrow{P}+\overrightarrow{Q}$
Since $\overrightarrow{R}$ makes angle ${45}^{\circ }$ with $\overrightarrow{P}$ and $\overrightarrow{Q}$ respectively, the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ${45}^{\circ }+{45}^{\circ }={90}^{\circ }$
Thus magnitude of resultant vector $|\overrightarrow{P}+\overrightarrow{Q}|=\sqrt{P^2+Q^2+2PQ\cos {90}^{\circ }}=\sqrt{P^2+Q^2}$