Question

What is the angle between $\overrightarrow{P}$ and the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$?

• A. $0^{\circ }$
• B. ${45}^{\circ }$
• C. ${90}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A $0^{\circ }$

Let the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$ is $\overrightarrow{R}$, then,

$\overrightarrow{R}=(\overrightarrow{P}+\overrightarrow{Q})+(\overrightarrow{P}-\overrightarrow{Q})=2\overrightarrow{P}$

$\Rightarrow \overrightarrow{R}$ and $\overrightarrow{P}$ are parallel vectors, so the angle between them is $0^{\circ }$.

Hence, option $\left(A\right)$ is the correct answer.