WAEC 2014 · Paper 2 · Q7

(a)
If the position vectors of $A$ and $B$ relative to the origin are $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ and $\begin{pmatrix} 5 \\ -2 \end{pmatrix}$ , find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$ .

Worked solution (try it first)

$\overrightarrow{OA} \cdot \overrightarrow{OB} = (4)(5) + (3)(-2)$
$= 20 - 6$
$= 14$ .
$|\overrightarrow{OA}| = 5$ and $|\overrightarrow{OB}| = \sqrt{29}$ .
$\cos\theta = \dfrac{14}{5\sqrt{29}}$
$\approx 0.5200$ , so $\theta \approx 58.67^\circ$ .