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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA3 Marks
Question
Find the unit vector in the direction of sum of vectors $\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{j}}+\hat{\text{k}}.$
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Answer

Let $\vec{\text{c}}$ denote the sum of vectors $\vec{\text{a}}$ and $\vec{\text{b}}.$
Thus $\vec{\text{c}}=\vec{\text{a}}+\vec{\text{b}}=2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}+2\hat{\text{j}}+\hat{\text{k}}$
$=2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$
Now, we know that, unit vector in the direction of a vector $\vec{\text{a}}$ is given as $\frac{\vec{\text{a}}}{|\vec{\text{a}}|}.$
$\therefore$ unit vector in the direction of $\vec{\text{c}}=\frac{\vec{\text{c}}}{|\vec{\text{c}}|}=\frac{2\hat{\text{i}}+\hat{\text{j}}+\hat{2\text{k}}}{\sqrt{2^2+1^1+2^2}}$
$=\frac{2\hat{\text{i}}+\hat{\text{j}}+\hat{2\text{k}}}{\sqrt{9}}$
Thus, $\vec{\text{c}}=\frac{2\hat{\text{i}}+\hat{\text{j}}+\hat{2\text{k}}}{3}$

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