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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
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:
  1. $\frac{\pi}{6}$
  2. $\frac{\pi}{3}$
  3. $\frac{\pi}{2}$
  4. $\frac{5\pi}{2}$
✓

Answer

  1. $\frac{\pi}{3}$

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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