Question

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

Answer 1

Given:
$$\begin{gathered} \overrightarrow{b}=2\hat{i}+\hat{j}+2\hat{k} \\ \left|\overrightarrow{b}\right|=\sqrt{2^2+1^2+2^2}=\sqrt{4+1+4}=\sqrt{9}=3 \end{gathered}$$
∴ Unit vector = $\frac{\overrightarrow{b}}{\left|\overrightarrow{b}\right|}=\frac{1}{3}\left(2\hat{i}+\hat{j}+2\hat{k}\right)=\frac{2}{3}\hat{i}+\frac{1}{3}\stackrel{⏜}{j}+\frac{2}{3}\hat{k}$