Physics - Vectors Question with Solution | TestHub

For two vectors to be perpendicular, their dot product is equal to zero.

So, $\overrightarrow{P}·\overrightarrow{Q}=0$

$$\begin{gathered} \Rightarrow \left(\hat{\mathrm{i}}+2m\hat{\mathrm{j}}+m\hat{\mathrm{k}}\right)·\left(4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+m\hat{\mathrm{k}}\right)=0 \\ \Rightarrow 4-4m+m^2=0 \\ \Rightarrow {\left(m-2\right)}^2=0 \\ \Rightarrow m=2 \end{gathered}$$