Question

If $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{P}-\overrightarrow{Q}$ and q is the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$, then

• A. $q=0^{\circ }$
• B. $q={90}^{\circ }$
• C. $P=0$
• D. $Q=0$

Answer 1

The correct option is B $q={90}^{\circ }$

Let $\overrightarrow{p},\overrightarrow{q}$ represents forces $p$ and $Q$.

$\begin{array}{c}\therefore \left|\overrightarrow{p}+\overrightarrow{q}\right|=\left|\overrightarrow{p}-\overrightarrow{q}\right|\\ \left|\overrightarrow{p}\right|+\left|\overrightarrow{q}\right|+2\overrightarrow{p}\overrightarrow{q}={\left|\overrightarrow{p}\right|}^2+{\left|\overrightarrow{q}\right|}^2-2\overrightarrow{p}\overrightarrow{q}\\ \Rightarrow \frac{4\overrightarrow{p}.\overrightarrow{q}}{\overrightarrow{p}.\overrightarrow{q}}=0\\ \Rightarrow \overrightarrow{p}.\overrightarrow{q}=0=\cos {90}^0\\ \therefore Angleis{90}^0\end{array}$

Hence, Option $B$ is correct.