Question

Find unit vector in the direction of vector $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$

Answer 1

Given vector is a $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$

Magnitude of $\overrightarrow{a}=|\overrightarrow{a}|=\sqrt{2^2+3^2+1^2}$

$\Rightarrow |\overrightarrow{a}|=\sqrt{4+9+1}$

$\Rightarrow |\overrightarrow{a}|=\sqrt{14}$

Unit vector in the direction of $\overrightarrow{a}$ is

$\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}$

$\hat{a}=\frac{1}{\sqrt{14}}[2\hat{i}+3\hat{j}+\hat{k}]$

$\hat{a}=\frac{2\hat{i}}{\sqrt{14}}+\frac{3\hat{j}}{\sqrt{14}}+\frac{\hat{k}}{\sqrt{14}}$