# If $\overrightarrow{a}$ and $\overrightarrow{b}$ include an angle $120^{\circ}$ and their magnitude are $2$ and $\sqrt{3}$ then $\overrightarrow{a} .\overrightarrow{b}$ is equal to

$\begin{array}{1 1}(1)\sqrt{3}& (2)-\sqrt{3} \\(3)2& (4)-\large\frac{\sqrt{3}}{2}\end{array}$

Given $\overrightarrow{a}=2$ and $\overrightarrow{a}=2$
Angle between $\overrightarrow{a}=2$ and $\overrightarrow{b}$ is $120^{\circ}$
$\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}| \cos 120^{\circ}$
$\qquad= 2 \times \sqrt 3 \cos (180^{\circ} -60^{\circ})$
$\qquad= 2 \times \sqrt 3 \times \cos 60^{\circ}$
$\qquad= -2 \times \sqrt 3 \times \large \frac{1}{2}$
$\qquad=-\sqrt{3}$
Hence 2 is the correct answer.