Q101 / 200 · NEET 2007 · Physics
$\vec{A}$ 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.
- A$45^{\circ}$
- B$30^{\circ}$
- C$90^{\circ}$
- Correct answerD$60^{\circ}$
Solution
Finding the angle between the vectors:
\(\begin{aligned}
& |\mathrm{A} \times \mathrm{B}|=\sqrt{3}(\mathrm{AB}) \\
& |\mathrm{A}||\mathrm{B}| \sin (\theta)=\sqrt{3}|\mathrm{~A}||\mathrm{B}| \cos (\theta)
\end{aligned}\)
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 \(60^{\circ}\)
Hence, the correct answer is option: 'D'.