Question

Write a vector in the direction of vector $5\hat{i}-\hat{j}+2\hat{k}$ which has magnitude of 8 unit.

Answer 1

Given:
$$\begin{gathered} \overrightarrow{a}=5\hat{i}-\hat{j}+2\hat{k} \\ \left|\overrightarrow{a}\right|=\sqrt{5^2+{\left(-1\right)}^2+2^{{}^2}} \end{gathered}$$
$=\sqrt{25+1+4}=\sqrt{30}$
∴ Position Vector in the direction of ​vector $=8\times \frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{8}{\sqrt{30}}\left(5\hat{i}-\hat{j}+2\hat{k}\right)$