Question

Find the unit vector in the direction of $3\hat{i}+4\hat{j}-12\hat{k}.$

Answer 1

Let $\overrightarrow{a}=3\hat{i}+4\hat{j}-12\hat{k}$
Then, $\left|\overrightarrow{a}\right|=\sqrt{3^2+4^2+{\left(-12\right)}^2}=\sqrt{9+16+144}=\sqrt{169}=13$
So, a unit vector in the direction of $\overrightarrow{a}$ is given by
$\hat{a}=\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{1}{13}\left(3\hat{i}+4\hat{j}-12\hat{k}\right)=\frac{3}{13}\hat{i}+\frac{4}{13}\hat{j}-\frac{12}{13}\hat{k}$