Question

Let $\overrightarrow{A}=A\cos \theta \hat{i}+A\sin \theta \hat{j}$ be any vector. Another vector $\overrightarrow{B}$ which is perpendicular to $\overrightarrow{A}$ can be expressed as

• A. $B\cos \theta \hat{i}-B\sin \theta \hat{j}$
• B. $B\sin \theta \hat{i}-B\cos \theta \hat{j}$
• C. $B\cos \theta \hat{i}+B\sin \theta \hat{j}$
• D. $B\sin \theta \hat{i}+B\cos \theta \hat{j}$

Answer 1

The correct option is B $B\sin \theta \hat{i}-B\cos \theta \hat{j}$


$\overrightarrow{B}$ can be either of direction shown possible $\overrightarrow{B}$ is
$\overrightarrow{B}=B\cos \theta \hat{j}-B\sin \theta \hat{i}$
(or)
$\overrightarrow{B}=B\sin \theta \hat{i}-B\cos \theta \hat{j}$