Question

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

• A. zero
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

3

Given, perpendicular, implies $\overrightarrow{P}.\overrightarrow{Q}=0$
or, $(a\hat{i}+a\hat{j}+3\hat{k}).(a\hat{i}-2\hat{j}-\hat{k})=0$
or, $a^2-2a-3=0$
Solving the quadratic, we get, $a=3$ or $-1$.

Positive value is thus $3$.