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Scalar Or Dot Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
Write the projection of the vector $7\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}}$ on the vector $2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}.$
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Answer

Let $\vec{\text{a}}=7\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}};\vec{\text{b}}=2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}$
The projection of $\vec{\text{a}}$ on $\vec{\text{b}}$ is
$\Bigg(\frac{\vec{\text{a}}\vec{\text{b}}}{\big|\vec{\text{b}}\big|}\Bigg)$
$=\frac{\big(7\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}}\big).\big(2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}\big)}{\big|2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}\big|}$
$=\frac{14+6-12}{\sqrt{4+36+9}}$
$=\frac{8}{7}$

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