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Vector or Cross Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product3 Marks
Question
Find the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b},}$ if $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\vec{\text{a}}.\vec{\text{b}}.$
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Answer

Let $\theta$ be the angle between $\vec{\text{a}}$ and $\vec{\text{b}. }$
Given:
$\big|\vec{\text{a}}\times\vec{\text{b}}\big|=\vec{\text{a}}.\vec{\text{b}}$
$\Rightarrow|\vec{\text{a}}|\big|\vec{\text{b}}\big|\sin\theta=|\vec{\text{a}}|\big|\vec{\text{b}}\big|\cos\theta$
$\Rightarrow\sin\theta=\cos\theta$
$\Rightarrow\tan\theta=1$
$\Rightarrow\theta=\frac{\pi}{4}$

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