WAEC 2018 · Paper 2 · Q7

(a)
Given that $\mathbf m = 3\mathbf i - 2\mathbf j$ , $\mathbf n = 2\mathbf i + 3\mathbf j$ and $\mathbf p = -\mathbf i + 6\mathbf j$ , find $|4\mathbf m + 2\mathbf n - 3\mathbf p|$ .

Worked solution (try it first)

$4\mathbf m + 2\mathbf n - 3\mathbf p = (12 + 4 + 3)\mathbf i + (-8 + 6 - 18)\mathbf j$ .
$= 19\mathbf i - 20\mathbf j$ .
Its magnitude is $\sqrt{361 + 400} = \sqrt{761}$
$\approx 27.586$ .