Question

$\text{A}$ and $\text{B}$ are two vectors and $\theta$ is the angle between them,if $\text{A×B=}\sqrt{3}\text{(AB)}$ the value of $\text{θ}$ is

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

Answer 1

The correct option is A

$60°$

Finding the angle between the vectors :

$\left|\text{A×B}\right|=\sqrt{3}(\text{AB)}$

$\left|\text{A}\right|\left|\text{B}\right|\sin \left(\text{θ}\right)=\sqrt{3}\left|\text{A}\right|\left|\text{B}\right|\cos \left(\text{θ}\right)$

Cancelling both sides we get

$\sin \left(\text{θ}\right)=\sqrt{3}\cos \left(\text{θ}\right)$

$$\begin{gathered} \frac{\sin \left(\text{θ}\right)}{\cos \left(\text{θ}\right)}=\sqrt{3} \\ \tan \left(\text{θ}\right)=\sqrt{3} \end{gathered}$$

Hence $\text{θ=60°}$

Hence the angle between $\text{A}$ and $\text{B}$ is $60°$

So option(A) is the correct answer and all other options are incorrect answers .