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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 $\vec a$ and $\vec b$ with magnitudes $\sqrt 3 $ and 2, respectively, having $\vec a\;.\vec b = \sqrt 6 $
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Answer

$ \left| {\overrightarrow a } \right| = \sqrt 3 ,\left| {\overrightarrow b } \right| = 2,\overrightarrow a .\overrightarrow b = \sqrt 6 ,$

$\Rightarrow \overrightarrow a .\overrightarrow b = \left| {\overrightarrow a } \right|.\left| {\overrightarrow b } \right|\cos \theta \Rightarrow \sqrt 6$

$ = 2\sqrt 3 \cos \theta$

$\Rightarrow \cos \theta = \frac{1}{{\sqrt 2 }} \Rightarrow \theta = \frac{\pi }{4} $

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