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
$\mathbf{v} = \binom{t}{-4}$ , where $t$ is a positive number, and $|\mathbf{v}| = 5$ .

(a) Find the value of $t$ .

(b) Write down the value of $|-5\mathbf{v}|$ .
Level 5 · 4 marksTry it
2
$A$ is the point $(-3, 5)$ and $B$ is the point $(7, -1)$ .

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

(b) $C$ is the point such that $\overrightarrow{BC} = \tfrac12\overrightarrow{AB}$ . Find the coordinates of $C$ .

(c) Work out $|\overrightarrow{AC}|$ , giving your answer correct to $1$ decimal place.
Level 5 · 7 marksTry it
3
$\mathbf{p} = \begin{pmatrix} 2x \\ 5 \end{pmatrix} + \begin{pmatrix} y \\ -3 \end{pmatrix}$ $\qquad$ $\mathbf{q} = \begin{pmatrix} x \\ 2 \end{pmatrix} + \begin{pmatrix} 3y \\ 1 \end{pmatrix}$

$\mathbf{p}$ is parallel to $\mathbf{q}$ .

Express $y$ in terms of $x$ .

(3 marks)
Level 5 · 3 marksTry it