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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA3 Marks
Question
Find the angle between the vectors $\vec{\text{a}}+\vec{\text{b}}\text{ and }\vec{\text{a}}-\vec{\text{b}}\text{ if }\text{ }\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}\text{ and }\vec{\text{b}}\text{ }=3\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}.$
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Answer

Let = $\vec{\text{p}}=\vec{\text{a}}+\vec{\text{b}}=\Big(5\hat{\text{i}}+\hat{\text{k}}\Big),\text{ }\vec{\text{p}}=\vec{\text{a}}+\vec{\text{b}}=\Big(-\hat{\text{i}}+2\hat{\text{j}}+5\hat{\text{k}}\Big)$
$\text{Using }\text{ }\cos\theta=\frac{\vec{\text{p}}\cdot\vec{\text{q}}}{|\vec{\text{p}}||\vec{\text{q}}|},\text{we get}$
$\cos\theta=0\text{ }\Rightarrow\text{ }\theta=\frac{\pi}{2}.$

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