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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA2 Marks
Question
Find a vector in the direction of $\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$, which has magnitude of 6 units.
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Answer

Given:
$\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$
$|\vec{\text{a}}|=\sqrt{2^2+(-1)^2+2^2}$
$=\sqrt{4+1+4}$
$=\sqrt{9}$
$=3$
$\therefore$ Required Vector $=6\times\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=6\times\frac{\big(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}\big)}3$
$=4\hat{\text{i}}-2\hat{\text{j}}+4\hat{\text{k}}$

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