GCSE Mathematics · Edexcel 1MA1 · Topic G.3

Vectors

Key points

A vector has size and direction. Write it as a column vector, e.g. $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ , or in bold/underlined letters such as $\mathbf{a}$ .
Add and subtract column vectors by adding or subtracting their components; multiply by a scalar by multiplying each component.
$\overrightarrow{AB}$ means the journey from $A$ to $B$ ; $\overrightarrow{BA} = -\overrightarrow{AB}$ .
To find a vector between two points, follow a known route: $\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC}$ .
Vectors that are multiples of each other are parallel. If $\overrightarrow{AB} = k\overrightarrow{BC}$ and they share point $B$ , then $A$ , $B$ and $C$ are collinear.
For a point dividing a line in a ratio, e.g. $M$ the midpoint of $AB$ , $\overrightarrow{AM} = \frac{1}{2}\overrightarrow{AB}$ .
Vector proof questions (higher): write every vector in terms of $\mathbf{a}$ and $\mathbf{b}$ , simplify, then state the conclusion.

Topic notesPremium

A vector describes a movement: how far and in which direction. Foundation tier covers column vector arithmetic and diagrams; Higher tier uses vectors to describe routes around a shape and prove geometric facts.

Unlock the full notes with Premium

Premium includes full topic notes, the paper generator, self-quizzes and progress tracking.

See Premium plans Already Premium? Sign in

Practise this topicPremium

Premium members can generate an exam-style paper with a mark scheme, or take a quick quiz, on Vectors.

Back to all Mathematics topics