GCSE · Vectors

Vectors on a shapeExam-style questions

Expressing any journey around a figure in terms of two given vectors — why every route gives the same answer, why going against an arrow flips the sign, and why a point splitting a side in the ratio 2:3 sits two fifths along, not two thirds.

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$PQRS$ is a parallelogram.

$\overrightarrow{PQ} = \mathbf{a}$ and $\overrightarrow{PS} = \mathbf{b}$ .The diagram is a sketch and is not accurately drawn.

(a) Write down, in terms of $\mathbf{a}$ and/or $\mathbf{b}$ , the vector $\overrightarrow{SR}$ .

(b) Give a reason for your answer to part (a).

(c) Find $\overrightarrow{QS}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ .
Level 2 · 4 marksTry it
2
$OAB$ is a triangle. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ .

$M$ is the midpoint of $AB$ .The diagram is a sketch and is not accurately drawn.

(a) Find $\overrightarrow{AB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ .

(b) Find $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , giving your answer in its simplest form.
Level 3 · 4 marksTry it
3
$ABCD$ is a trapezium. $\overrightarrow{AB} = \mathbf{a}$ and $\overrightarrow{BC} = \mathbf{b}$ .

$AD$ is parallel to $BC$ , and $AD = 3 \times BC$ .The diagram is a sketch and is not accurately drawn.

(a) Write down $\overrightarrow{AD}$ in terms of $\mathbf{b}$ .

(b) Find $\overrightarrow{DC}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , giving your answer in its simplest form.
Level 3 · 4 marksTry it
4
$ABCD$ is a quadrilateral.

$\overrightarrow{AB} = \mathbf{a}$ , $\overrightarrow{BC} = \mathbf{b}$ and $\overrightarrow{CD} = 2\mathbf{b} - \mathbf{a}$ .The diagram is a sketch and is not accurately drawn.

(a) Find $\overrightarrow{AD}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , giving your answer in its simplest form.

(b) Find $\overrightarrow{DB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , giving your answer in its simplest form.
Level 3 · 4 marksTry it
5
$OAB$ is a triangle. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ .

$M$ is the midpoint of $AB$ .

(a) Write $\overrightarrow{AB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ . (1 mark)

(b) Write $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ . Give your answer in its simplest form. (2 marks)
Level 3 · 3 marksTry it

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