Question

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

Answer 1

Given: $\overrightarrow{a}=3\hat{i}-2\hat{j}+6\hat{k}$
Then,
$\overrightarrow{\left|a\right|}=\sqrt{3^2+{\left(-2\right)}^2+6^2}=\sqrt{9+4+36}=\sqrt{49}=7$

∴ Unit vector = $\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{3\hat{i}-2\hat{j}+6\hat{k}}{7}$ $=\frac{3}{7}\hat{i}-\frac{2}{7}\hat{j}+\frac{6}{7}\hat{k}$