Question

Find a vector in the direction of a vector $\overrightarrow{a}=\hat{i}-\hat{j}+\hat{k}$, which has magnitude 8 units.

Answer 1

Given, $\overrightarrow{a}=\hat{i}-\hat{j}+\hat{k}$

Now, unit vector in the direction of $\overrightarrow{a}$ is

$\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}=\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}$

Therefore, vector of magnitude 8 units in the direction of $\hat{a}$

$=\frac{8}{\sqrt{3}}\hat{i}-\frac{8}{\sqrt{3}}\hat{j}+\frac{8}{\sqrt{3}}\hat{k}$