Choose the correct answer from the given four options. The angle … - Vidyadip

MCQ

Choose the correct answer from the given four options. The angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ with magnitudes $\sqrt{3}$ and $4,$ respectively, and $\vec{\text{a}}\cdot\vec{\text{b}}=2\sqrt{3}$ is:

A
$\frac{\pi}{6}$
✓
$\frac{\pi}{3}$
C
$\frac{\pi}{2}$
D
$\frac{5\pi}{2}$

✓

Answer

Correct option: B.

$\frac{\pi}{3}$

Here, $|\vec{\text{a}}|=\sqrt{3},|\vec{\text{b}}|=4$ and $\vec{\text{a}}\cdot\vec{\text{b}}=2\sqrt{3} [$given$]$
We know that, $\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}||\vec{\text{b}}|\cos\theta$
$\Rightarrow2\sqrt{3}=\sqrt{3}.4.\cos\theta$
$\Rightarrow\cos\theta=\frac{2\sqrt{3}}{4\sqrt{3}}=\frac{1}{2}$
$\therefore\theta=\frac{\pi}{3}$

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