Question

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

• A. $3$
• B. $4$
• C. $9$
• D. $1$

Answer 1

The correct option is A $3$

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