Question

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

• A. 3
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (A)

3

Answer 2

Vector $\vec{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and vector $\vec{Q=}a\hat{i}-2\hat{j}-\hat{k}.$ If two vectors are perpendicular to each other, then $\vec{P}\times\vec{Q}=0$ or $\left(a\hat{i}+a\hat{j}+3\hat{k}\right)\times\left(a\hat{i}-2\hat{j}-\hat{k}\right)=0$ or $a^{2}-2a-3=0.$ Solving this quadratic equation, we get $a = 3$ or $-1$. Therefore positive value of $a$ is $3$.