Question

Find the unit vector in the direction of $3\hat{i}-6\hat{j}+2\hat{k}$.

Answer 1

Let $\overrightarrow{a}=3\hat{i}-6\hat{j}+2\hat{k}$. Then,

$|\overrightarrow{a}|=\sqrt{3^2+(-6{)}^2+2^2}=\sqrt{49}=7$

So, a unit vector in the direction of $\overrightarrow{a}$ is given by

$\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}=\frac{1}{7}(3\hat{i}-6\hat{j}+2\hat{k})=\frac{3}{7}\hat{i}-\frac{6}{7}\hat{j}+\frac{2}{7}\hat{k}$