Question

Which of the following expression is equal to $\cos \theta$, where $\theta$ is angle between $\overrightarrow{A}\text{and}\overrightarrow{B}$?

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

Answer 1

The correct option is D $\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$

Dot product of two vectors is ,
$\overrightarrow{A}\cdot \overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta$
$\therefore$ $\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$= $\cos \theta$