Question

Write a unit vector in the direction of $\overrightarrow{a}=3\hat{i}+2\hat{j}+6\hat{k}.$

Answer 1

We have,
$$\begin{gathered} \overrightarrow{a}=3\hat{i}-2\hat{j}+6\hat{k} \\ \left|\overrightarrow{a}\right|=\sqrt{3^2+{\left(-2\right)}^2+6^2}=\sqrt{9+4+36}=\sqrt{49}=7 \end{gathered}$$

∴ Unit vector in the direction of $\overrightarrow{a}$ = $\hat{a}=\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{1}{7}\left(3\hat{i}-2\hat{j}+6\hat{k}\right)=\frac{3}{7}\hat{i}-\frac{2}{7}\hat{j}+\frac{6}{7}\hat{k}$