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
$OAB$ is a triangle. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ .

The point $P$ lies on $AB$ so that $AP:PB = 1:4$ .The diagram is a sketch and is not accurately drawn.

Find $\overrightarrow{OP}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ , giving your answer in its simplest form.
Level 4 · 4 marksTry it
2
$OABC$ is a trapezium. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OC} = \mathbf{b}$ .

$CB$ is parallel to $OA$ , and $CB = 3 \times OA$ .

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

(a) Find $\overrightarrow{OB}$ 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 4 · 5 marksTry it
3
$OAB$ is a triangle. $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ .

$P$ is the point on $AB$ such that $AP : PB = 2 : 1$ . $M$ is the midpoint of $OB$ .

(a) Find $\overrightarrow{OP}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ . Give your answer in its simplest form. [3]

(b) Find $\overrightarrow{PM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ . Give your answer in its simplest form. [2]
Level 4 · 5 marksTry it