WAEC 2020 · Paper 2 · Q7

Vectors

If $\mathbf{p} = 2\mathbf{i} + 4\mathbf{j}$ and $\mathbf{q} = 3\mathbf{i} + \mathbf{j}$ , find the magnitude and direction of the resultant of $\mathbf{p}$ and $\mathbf{q}$ .

(a)
Magnitude (2 d.p.)
(b)
Direction (degrees from the positive $x$ -axis)

Try it on a graph

Head-to-tail: p then q lands at the same point as the resultant.

Worked solution (try it first)

$\mathbf p + \mathbf q = (2 + 3)\mathbf i + (4 + 1)\mathbf j$
$= 5\mathbf i + 5\mathbf j$ .

(a)

$|\mathbf p + \mathbf q| = \sqrt{25 + 25}$
$= \sqrt{50}$
$\approx 7.07$ .

(b)

$\tan\theta = \frac55 = 1$ , so $\theta = 45^\circ$ above the positive $x$ -axis (a bearing of $045^\circ$ ).

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