WAEC 2023 · Paper 1 · Q26

Calculate, correct to one decimal place, the angle between $5\mathbf{i} + 12\mathbf{j}$ and $-2\mathbf{i} + 3\mathbf{j}$ .

Worked solution (try it first)

The dot product is $5(-2) + 12(3) = -10 + 36 = 26$ .
The lengths are $\sqrt{25 + 144} = 13$ and $\sqrt{4 + 9} = \sqrt{13}$ .
$\cos\theta = \dfrac{26}{13\sqrt{13}}$ , which simplifies to $\dfrac{2}{\sqrt{13}} = 0.5547$ .
So $\theta = 56.3^\circ$ , option B.