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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

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

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Given $\overrightarrow{a}=2 $ and $\overrightarrow{a}=2 $
Angle between $\overrightarrow{a}=2$ and $\overrightarrow{b}$ is $120^{\circ}$
$\overrightarrow{a}.\overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}| \cos 120^{\circ}$
$\qquad= 2 \times \sqrt 3 \cos (180^{\circ} -60^{\circ})$
$\qquad= 2 \times \sqrt 3 \times \cos 60^{\circ}$
$\qquad= -2 \times \sqrt 3 \times \large \frac{1}{2}$
Hence 2 is the correct answer.
answered May 5, 2014 by meena.p

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