Question

If two vectors $\vec{ P }=\hat{i}+2 m \hat{j}+m \hat{k}$ and $\vec{Q}=4 \hat{i}-2 \hat{j}+m \hat{k}$ are perpendicular to each other. Then, the value of $m$ will be :

• A. -1
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (B)

$ \vec{P} \cdot \vec{Q}=0 $
$(\hat{i}+2 m \hat{j}+m \hat{k}) \cdot(4 \hat{i}-2 \hat{j}+m \hat{k})-0 $
$ \Rightarrow 4-4 m+m^2=0 $
$ \Rightarrow(m-2)^2=0 \Rightarrow m=2$