Question

If $\overrightarrow{A}\cdot \overrightarrow{B}=|\overrightarrow{A}\times \overrightarrow{B}|$, then what is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

• A. $0^{\circ }$
• B. ${45}^{\circ }$
• C. ${90}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

We know that,

$\overrightarrow{A}\cdot \overrightarrow{B}=AB\cos \theta$

$|\overrightarrow{A}\times \overrightarrow{B}|=AB\sin \theta$

Given, $\overrightarrow{A}\cdot \overrightarrow{B}=|\overrightarrow{A}\times \overrightarrow{B}|$

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

$\Rightarrow \tan \theta =1$

$\Rightarrow \theta ={45}^{\circ }$

Hence, option $\left(B\right)$ is the correct answer.