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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 1 and 2 respectively and when $\vec{a} \cdot \vec{b}=1$.
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Answer

Given $\vec{a} \cdot \vec{b}=1,|\vec{a}|=1$ and $|\vec{b}|=2$. We have
$\theta=\cos ^{-1}\left(\frac{\vec{a} \cdot \vec{b}}{|\vec{a} \| \vec{b}|}\right)=\cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}$

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