Question

Which of the following is the unit vector perpendicular to $\overrightarrow{A}$ and $\overrightarrow{B}$.

• A. $\frac{\overbrace{A}\times \hat{B}}{AB\sin \theta }$
• B. $\frac{\hat{A}\times \hat{B}}{AB\cos \theta }$
• C. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{AB\sin \theta }$
• D. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{AB\cos \theta }$

Answer 1

The correct option is C

$\frac{\overrightarrow{A}\times \overrightarrow{B}}{AB\sin \theta }$

Explanation:

Vector perpendicular to $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\overrightarrow{A}\times \overrightarrow{B}=AB\sin \theta \hat{n}$

Unit vector perpendicular to A and B is given by

$\overbrace{n}=\frac{\overrightarrow{A}\times \overrightarrow{B}}{\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\sin \theta }$= $\frac{\overrightarrow{A}\times \overrightarrow{B}}{AB.\sin \theta }$

Thus, option C is the correct option.