Question

If $\overrightarrow{P}\times \overrightarrow{Q}=\overrightarrow{Q}\times \overrightarrow{P}$, the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\theta (0^{\circ }<\theta <{360}^{\circ })$. The value of ${}^{\prime }{\theta }^{\prime }$ will be ____(in degrees).

Answer 1

If $\overrightarrow{P}\times \overrightarrow{Q}=\overrightarrow{Q}\times \overrightarrow{P}$
$\Rightarrow \overrightarrow{P}\times \overrightarrow{Q}=-\overrightarrow{P}\times \overrightarrow{Q}$
$\Rightarrow 2(\overrightarrow{P}\times \overrightarrow{Q})=0$
Or $\overrightarrow{P}\times \overrightarrow{Q}=0$
Only if $\overrightarrow{P}=0$ or $\overrightarrow{Q}=0$
Or the angle b/w $\overrightarrow{P}$ and $\overrightarrow{Q}$ is ${180}^{\circ }$ $\theta (0^{\circ }<\theta <{360}^{\circ })$
So, $\theta ={180}^{\circ }$