NECO 2023 · Paper 1 · Q31

Find the unit vector in the direction of $\mathbf{r} = 15\mathbf{i} + 16\mathbf{j} - 12\mathbf{k}$ .

Worked solution (try it first)

Find the length: $|\mathbf r| = \sqrt{15^2 + 16^2 + (-12)^2}$
$= \sqrt{225 + 256 + 144}$ .
That is $\sqrt{625} = 25$ .
Divide $\mathbf r$ by its length: $\hat{\mathbf r} = \frac{1}{25}(15\mathbf i + 16\mathbf j - 12\mathbf k)$ , option A.