Fiducia TogetherVectors
A quantity with size and direction, written as a column or with an arrow.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A vector has magnitude and direction, written as a column of two numbers or as a letter with an arrow. Scalars have magnitude only.
Where it applies
Higher tier maths, and physics throughout.
How it works
Adding vectors is adding the components; multiplying by a scalar scales both components. Two vectors are parallel if one is a multiple of the other, which is the standard proof route.
In geometry problems, a path is expressed as a sum of vectors along the route taken.
How to use it in your work
Write every journey as a sum of named vectors before simplifying — the method marks are in the route.
To prove points are collinear, show one vector is a multiple of another AND that they share a point. Both halves are needed.
Where to get help
Your teacher and your board's specification. Bitesize for worked examples, and the subject song for the topic list.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.