Question

Find a vector in the direction of $\overrightarrow{a}=2\hat{i}-\hat{j}+2\hat{k},$ which has magnitude of 6 units.

Answer 1

Given:
$$\begin{gathered} \overrightarrow{a}=2\hat{i}-\hat{j}+2\hat{k} \\ \left|\overrightarrow{a}\right|=\sqrt{2^2+{\left(-1\right)}^2+2^2}=\sqrt{4+1+4}=\sqrt{9}=3 \end{gathered}$$
∴ Required Vector $=6\times \frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=6\times \frac{\left(2\hat{i}-\hat{j}+2\hat{k}\right)}{3}=4\hat{i}-2\hat{j}+4\hat{k}$