Question

Let $\overrightarrow{A}=Acos\theta \hat{i}+Asin\theta \hat{j}$ be any vector.Then another vector $\overrightarrow{B}$ which is normal to $\overrightarrow{A}$ can be?

• A. B cos + B sin
• B. B sin + B cos
• C. B sin - B cos
• D. B cos - B sin

Answer 1

The correct option is C

B sin - B cos

Dot product of two perpendicular vectors is zero

$\therefore$ We need a vector $\overrightarrow{B}$ such that,$\overrightarrow{A}$.$\overrightarrow{B}$ = 0 If we consider option (c)

$\overrightarrow{A}$.$\overrightarrow{B}$ = AB sin$\theta$cos$\theta$

= 0

$\therefore$ Answer is (C)