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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA2 Marks
Question
Find the angle between two vectors $\vec{a}\ \text{and}\ \vec{b}$ with magnitudes $\sqrt{3}\ \text{and}\ 2,$ respectively having $\vec{a}\cdot\vec{b}=\sqrt{6}.$
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Answer

$\text{Given:}\ \ \big|\vec{a}\big|=\sqrt{3},\Big|\vec{b}\Big|=2\ {\text{and}}\ \vec{a}.\vec{b}=\sqrt{6}$ Let $\theta$ be the angle between the vector $\vec{a}\ \text{and}\ \vec{b}.$ We know that $\text{cos}\ \theta=\frac{\vec{a}.\vec{b}}{\big|\vec{a}\big|.\big|\vec{b}\big|}$$\Rightarrow\ \ \text{cos}\ \theta=\frac{\sqrt{6}}{\sqrt{3}.2}=\frac{\sqrt{3}.\sqrt{2}}{\sqrt{3}.\sqrt{2}.\sqrt{2}}=\frac{1}{\sqrt{2}}$ $\Rightarrow\ \ \text{cos}\ \theta=\text{cos}\frac{\pi}{4}$
$\Rightarrow\ \theta= \frac{\pi}{4}$

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