Mathematics In Physics Question 2
Question 2 - 24 January - Shift 2
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 :
(1) 1
(2) -1
(3) -3
(4) 2
Show Answer
Answer: (4)
Solution:
$\overrightarrow{{}P} \cdot \overrightarrow{{}Q}=0$
$(\hat{i}+2 m \hat{j}+m \hat{k}) \cdot(4 \hat{i}-2 \hat{j}+m \hat{k})=0$
$\Rightarrow 4-4 m+m^{2}=0$
$\Rightarrow(m-2)^{2}=0 \Rightarrow m=2$
