Question

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

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is A $3$

We know that,
If $\overrightarrow{A}\perp \overrightarrow{B},\overrightarrow{A}.\overrightarrow{B}=0$

$a^2-2a-3=0$
$(a+1)(a-3)=0$
$a=-1$ or $3$
Hence the positive value of $a=3$