WAEC 2022 · Paper 2 · Q8

(a)
Given that $\mathbf p = (8\text{ N}, 030^\circ)$ and $\mathbf q = (9\text{ N}, 150^\circ)$ , find, in component form, the unit vector along $(\mathbf p - \mathbf q)$ . (Give the $\mathbf i$ and $\mathbf j$ components to 4 d.p.)
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$\mathbf p$ : $8\sin30^\circ = 4$ east and $8\cos30^\circ = 6.928$ north.
$\mathbf q$ : $9\sin150^\circ = 4.5$ east and $9\cos150^\circ = -7.794$ north.
$\mathbf p - \mathbf q = -0.5\mathbf i + 14.722\mathbf j$ .
$|\mathbf p - \mathbf q| = \sqrt{0.25 + 216.74}$
$\approx 14.731$ .
Unit vector: $\dfrac{-0.5\mathbf i + 14.722\mathbf j}{14.731} \approx -0.0339\mathbf i + 0.9994\mathbf j$ .