Question

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

• A. 3
• B. 4
• C. 9
• D. 13

Answer 1

The correct option is A 3

$\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$
$\overrightarrow{Q}=a\hat{i}+2\hat{j}-\hat{k}$
$\overrightarrow{P}.\overrightarrow{Q}=0$
$a^2-2a-3=0$
$a^2-3a+a-3=0$
$a(a-3)+1(a-3)=0$
$a=-1,3$
Hence, 3 is the correct answer according to the question.