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If \( |\overrightarrow a|=\sqrt 3, |\overrightarrow b|=2\) and the angle between \( \overrightarrow a \: and \: \overrightarrow b\) is \( 60^{\circ}\), find \( \overrightarrow a.\overrightarrow b\)

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  • $\overrightarrow a.\overrightarrow b=\mid a\mid \mid b\mid\cos\theta$
Step 1:
Given :
$\mid \overrightarrow a\mid=3,\mid \overrightarrow b\mid=2$
$\theta =60^{\circ}$
$\therefore \overrightarrow a.\overrightarrow b=\mid \overrightarrow a\mid.\mid \overrightarrow b\mid \cos\theta$
Substituting the values we get,
$\overrightarrow a.\overrightarrow b=3\times 2\cos 60^{\circ}$
Step 2:
But $\cos 60^{\circ}=\large\frac{1}{2}$
$\therefore \overrightarrow a.\overrightarrow b=3\times 2\times \large\frac{1}{2}$
$\overrightarrow a.\overrightarrow b=3$units.
answered Sep 24, 2013 by sreemathi.v

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