WAEC 2017 · Paper 2 · Q8

(a)
Given that $\mathbf m = \begin{pmatrix} -12 \\ 5 \end{pmatrix}$ and $\mathbf n = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$ , find a vector $\mathbf p$ such that $|\mathbf p| = 35$ and $\mathbf p$ is in the direction of $\mathbf m - 5\mathbf n$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$\mathbf m - 5\mathbf n = \begin{pmatrix} -12 - 5 \\ 5 + 5 \end{pmatrix}$
$= \begin{pmatrix} -17 \\ 10 \end{pmatrix}$ .
Its length is $\sqrt{289 + 100} = \sqrt{389}$ .
$\mathbf p = \dfrac{35}{\sqrt{389}}\begin{pmatrix} -17 \\ 10 \end{pmatrix}$
$\approx \begin{pmatrix} -30.17 \\ 17.75 \end{pmatrix}$ .