Question

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

Answer 1

The unit vector ${\displaystyle \overrightarrow{a}}$  in the direction of vector  ${\displaystyle \overrightarrow{a}=\hat{i}+\hat{j}+2\hat{k}}$ is given by ${\displaystyle \overrightarrow{a}=\frac{\overrightarrow{a}}{\left|a\right|}}$.

${\displaystyle \left|\overrightarrow{a}\right|=\sqrt{1^2+1^2+2^2}}$

${\displaystyle =\sqrt{1+1+4}}$

${\displaystyle =\sqrt{6}}$

Unit vector in the direction of vector a,

${\displaystyle \therefore \hat{a}=\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}}$

${\displaystyle =\frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt{6}}}$

${\displaystyle =\frac{1}{\sqrt{6}}\hat{i}+\frac{1}{\sqrt{6}}\hat{j}+\frac{2}{\sqrt{6}}\hat{k}}$