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.

Start practising Read the lesson

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
$A$ is the point $(2, 7)$ and $B$ is the point $(9, 3)$ .

(a) Write $\overrightarrow{AB}$ as a column vector.

(b) Write down $\overrightarrow{BA}$ as a column vector.

(c) Work out $|\overrightarrow{AB}|$ , giving your answer correct to $1$ decimal place.
Level 3 · 5 marksTry it
2
A drone flies from $P$ to $Q$ , and then from $Q$ to $R$ .Figure 1 (not accurately drawn)

$\overrightarrow{PQ} = \binom{4}{3}$ and $\overrightarrow{QR} = \binom{-6}{1}$ .

(a) Write $\overrightarrow{PR}$ as a column vector.

(b) $P$ is the point $(1, 2)$ . Write down the coordinates of $R$ .

(c) Write down $\overrightarrow{RP}$ as a column vector.
Level 3 · 5 marksTry it