WAEC 2011 · Paper 2 · Q7

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

Worked solution (try it first)

$\mathbf n + 5\mathbf s = \begin{pmatrix} -12 + 5 \\ 5 - 5 \end{pmatrix}$
$= \begin{pmatrix} -7 \\ 0 \end{pmatrix}$ , of length 7.
Unit vector: $\frac17\begin{pmatrix} -7 \\ 0 \end{pmatrix} = \begin{pmatrix} -1 \\ 0 \end{pmatrix}$ .
$\mathbf q = 35\begin{pmatrix} -1 \\ 0 \end{pmatrix}$
$= \begin{pmatrix} -35 \\ 0 \end{pmatrix}$ .