Question

$\overrightarrow{A}$ and $\overrightarrow{B}$ are 2 non-zero vectors if $|\overrightarrow{A}|\times |\overrightarrow{B}|$ = $\overrightarrow{A}\cdot \overrightarrow{B}$. What is the angle between the two vectors?

Answer 1

Let angle between $2$ vector be $\theta$

Now,

Cross product is given as

$\overline{A}\times \overline{B}=|A||B|\sin \theta$ ------ $\left(1\right)$

Dot product is given as

$\overline{A}.\overline{B}=|A||B|\cos \theta$ --------- $\left(2\right)$

Now it is given that

$\overline{A}\times \overline{B}=\overline{A}.\overline{B}$

$\Rightarrow |A||B|\sin \theta =|A||B|\cos \theta$

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

$\Rightarrow \tan \theta =1$

$\Rightarrow \theta ={45}^o=\frac{\pi }{4}rad$