Question

The vector $\overline{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $\overline{Q}=a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of 'a' is

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (A)

3

$\overrightarrow{P}.\overrightarrow{Q}=0$
$\therefore (a\hat{i}+a\hat{j}+3\hat{k}).(a\hat{i}-2\hat{j}-\hat{k})=0$
$\Rightarrow a^2-2a-3=0$
$\Rightarrow a=3ora=-1$