Choose the correct answer from the given four options. The angle between two vectors a and b with magnitudes 3 and 4, respectively, and a b =23 is: 1. 6 2. 3 3. 2 4. 5 2

2. 3 Solution: Here, | a |=3,| b |=4 and a b =23 [given] We know that, a b =| a || b | 23=3.4. = 23 43 =1 2 = 3

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

Question

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:

$\frac{\pi}{6}$
$\frac{\pi}{3}$
$\frac{\pi}{2}$
$\frac{5\pi}{2}$

✓

Answer

$\frac{\pi}{3}$

Solution:
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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