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Vector or Cross Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product3 Marks
Question
If $\vec{\text{a}}=4\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{k}},$ then find $\big|2\hat{\text{b}}\times\vec{\text{a}}\big|.$
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Answer

Given:
$\vec{\text{a}}=4\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}}$
$2\vec{\text{b}}=2\hat{\text{i}}+0\hat{\text{j}}+4\hat{\text{k}}$
$2\vec{\text{b}}\times\vec{\text{a}}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\2&0&-4\\4&3&1 \end{vmatrix}$
$=(0+12)\hat{\text{i}}-(2+16)\hat{\text{j}}+(6-0)\hat{\text{k}}$
$=12\hat{\text{i}}-18\hat{\text{j}}+6\hat{\text{k}}$
$\Rightarrow\big|2\vec{\text{b}}\times\vec{\text{a}}\big|=\sqrt{12^2+(-18^2)+6^2}$
$=\sqrt{504}$

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