Question

If $\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\left|\overrightarrow{A}·\overrightarrow{B}\right|$, then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be

• A. $30°$
• B. $45°$
• C. $60°$
• D. $90°$

Answer 1

The correct option is B

$45°$

Find the angle between vector $\overrightarrow{A}$ and $\overrightarrow{B}$:

Given, $\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\left|\overrightarrow{A}·\overrightarrow{B}\right|$

$\Rightarrow$ $AB\sin \theta =AB\cos \theta$

$\Rightarrow$ $\tan \theta =1$

$\mathbf{\therefore }\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{45}\mathbf{°}$

Hence, option ‘B’ is Correct.