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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}.$
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Answer

$\text{Let}\ \vec{a}=\hat{i}+2\hat{j}+3\hat{k}.$
$\therefore\big|\vec{a}\big|=\sqrt{1^2+2^2+3^2}=\sqrt{1+4+9}=\sqrt{14}$
Hence, the direction cosoines of $\vec{a}\ \text{are}\ \bigg(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}}\bigg).$

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