Question

Two vectors $\overrightarrow{A}=2\hat{i}+\hat{j}$ and $\overrightarrow{B}=a\hat{i}-2\hat{j}$ are perpendicular to each other. The value of a is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

The vectors $\overrightarrow{A}=2\hat{i}+\hat{j}$

and $\overrightarrow{B}=a\hat{i}-2\hat{j}$

when they are perpendicular to each other $\cos 90°=0\sin 90°=1$

$A.B=AB\cos 90°A.B=0(2\hat{i}+\hat{j})(a\hat{i}-2\hat{j})=02a-2=0a=1$