GCSE · Vectors

Column vectorsExam-style questions

A vector is a translation — so far across, so far up — not a place. How to add, subtract and scale columns, why a scalar multiple is parallel, how Pythagoras gives the magnitude, and why the journey from A to B is destination minus start.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$\mathbf{a} = \binom{6}{-8}$ and $\mathbf{b} = \binom{-9}{12}$ .

(a) Work out $|\mathbf{a}|$ .

(b) Show that $\mathbf{b}$ is parallel to $\mathbf{a}$ .

(c) Hence write down the value of $|\mathbf{b}|$ .
Level 4 · 5 marksTry it
2
$\overrightarrow{AB} = \binom{6}{-4}$ and $B$ is the point $(4, -1)$ .

(a) Find the coordinates of $A$ .

(b) $M$ is the midpoint of $AB$ . Find the coordinates of $M$ .
Level 4 · 4 marksTry it
3
$\mathbf{a} = \binom{3}{-1}$ and $\mathbf{b} = \binom{-2}{5}$ .

(a) Work out $2\mathbf{a} - 3\mathbf{b}$ as a column vector.

(b) The vector $\binom{k}{20}$ is parallel to $\mathbf{b}$ . Find the value of $k$ .
Level 4 · 5 marksTry it
4
$\mathbf{a} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}$ $\qquad$ $\mathbf{b} = \begin{pmatrix} -1 \\ 3 \end{pmatrix}$

The vector $\begin{pmatrix} t + 2 \\ 3t \end{pmatrix}$ is parallel to the vector $\mathbf{a} + 2\mathbf{b}$

Find the value of $t$ .

(3 marks)
Level 4 · 3 marksTry it