Question

If $|\overrightarrow{A}|=4$, $|\overrightarrow{B}|=3$ and the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${30}^{\circ }$, then the scalar product of these two vectors is

• A. $4$
• B. $6$
• C. $6\sqrt{3}$
• D. $4\sqrt{3}$

Answer 1

The correct option is C $6\sqrt{3}$

Scalar prodect of two vectors is given as
$\overrightarrow{A}.\overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta$
$\Rightarrow 4\times 3\cos {30}^{\circ }=12\times \frac{\sqrt{3}}{2}=6\sqrt{3}$