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Vector or Cross Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product2 Marks
Question
If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=144$ and $|\vec{\text{a}}|=4,$ find $\big|\vec{\text{b}}\big|.$
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Answer

We know
$\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2$
$\Rightarrow144=4^2\big|\vec{\text{b}}\big|^2$
$\Rightarrow144=16\big|\vec{\text{b}}\big|^2$
$\Rightarrow\big|\vec{\text{b}}\big|^2=9$
$\Rightarrow\big|\vec{\text{b}}\big|=3$

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