$\vec{A}$ and $\overline{\mathrm{B}}$ are two vectors and $\theta$ is the angle between them, if…
$\vec{A}$ and $\overline{\mathrm{B}}$ are two vectors and $\theta$ is the angle between them, if $|\overrightarrow{\mathrm{A}} \times \overline{\mathrm{B}}|=$ $\sqrt{3}(\overrightarrow{\mathrm{A}} \cdot \overline{\mathrm{B}})$, the value of $\theta$ is.
$45^{\circ}$
$30^{\circ}$
$90^{\circ}$
$60^{\circ}$
Solution
Finding the angle between the vectors:
$\begin{aligned}
& |A \times B|=\sqrt{3}(AB) \\
& |A||B| \sin (\theta)=\sqrt{3}|A||B| \cos (\theta)
\end{aligned}$
Cancelling both sides we get
$\begin{aligned}
& \sin (\theta)=\sqrt{3} \cos (\theta) \\
& \frac{\sin (\theta)}{\cos (\theta)}=\sqrt{3} \\
& \tan (\theta)=\sqrt{3}
\end{aligned}$
Hence $\theta=60^{\circ}$
Hence the angle between A and B is $60^{\circ}$