Question

The unit vector along $\overrightarrow{A}\times \overrightarrow{B}$ is

• A. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|}$
• B. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|\sin \theta }$
• C. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|\cos \theta }$
• D. $\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|\sin \theta }$

Answer 1

The correct option is B $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|\sin \theta }$

We know,
$|\overrightarrow{A}\times \overrightarrow{B}|=|\overrightarrow{A}|\cdot |\overrightarrow{B}|\sin \theta$
A vector divided by it's own magnitude gives unit vector along itself.
$\therefore \frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}|\cdot |\overrightarrow{B}|\sin \theta }$ will be unit vector along $\overrightarrow{A}\times \overrightarrow{B}$.