Question

If vectors $\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $Q=a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other, then the positive value of a is

• A. zero
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is D 3

If $\overline{P}$ and $\overline{Q}$ are perpendicular to each other then, $\overline{P}.\overline{Q}=0$

(where vector $\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $Q=a\hat{i}-2\hat{j}-\hat{k}$

$(a\hat{i}+a\hat{j}+3\hat{k})(a\hat{i}-2\hat{j}-\hat{k})=0$

$a^2-2a-3=0\Rightarrow (a-3)(a+1)=0$

$a-3=0\Rightarrow a=3$ and $a=-1$