Question

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

• A. 3
• B. 2
• C. 1
• D. zero

Answer 1

Answer: (A)

Since, vectors $\vec{P}$ and $\vec{Q}$ are perpendicular to each other, it means $\vec{P}.\vec{Q}=PQ\cos \theta$ Here $\theta ={90}^o$ So, $\vec{P}.\vec{Q}=0$ $\therefore$ $(a\hat{i}+a\hat{j}+3\hat{k}).(a\hat{i}-2\hat{j}-\hat{k})=0$ $\Rightarrow$ $a^2-2a-3=0$ $a^2-3a+a-3=0$ $a(a-3)+1(a-3)=0$ $(a+1)(a-3)=0$ Therefore, positive value of $a=3$