WAEC 2020 · Paper 1 · Q18

Find the angle between $\mathbf{i} + 5\mathbf{j}$ and $5\mathbf{i} - \mathbf{j}$ .

Worked solution (try it first)

Use the dot product: $(\mathbf{i} + 5\mathbf{j}) \cdot (5\mathbf{i} - \mathbf{j}) = 1 \times 5 + 5 \times (-1)$ , which is $5 - 5 = 0$ .
$\cos\theta = \dfrac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|}$
$= 0$ , so the vectors are perpendicular.
So the angle is $90^\circ$ , option D.