A Level Maths: Vectors Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Straight Line Geometry — foundational coordinate geometry skills
- Surds — vector magnitudes often involve surd answers
- GCSE Maths Pythagoras — assumed for finding magnitudes
A Level Maths vectors introduces 2D vectors as quantities with magnitude and direction. You learn to add, subtract, and scale them, calculate magnitudes and unit vectors, and use vectors to solve geometric problems — proving collinearity, finding midpoints, and analysing shapes. Vectors are foundational for Vectors in 3-d and for the Mechanics topics later in the course.
You work with vectors in two forms: column vector notation and $\mathbf{i}, \mathbf{j}$ notation (with $\mathbf{i}$ and $\mathbf{j}$ as unit vectors along the $x$ and $y$ axes). You add vectors using the triangle and parallelogram laws, scale them by a scalar, and find the magnitude using Pythagoras. Position vectors locate points relative to the origin, and the displacement from $A$ to $B$ is the position vector of $B$ minus the position vector of $A$. You use vectors to prove that lines are parallel (one vector is a scalar multiple of the other), that points are collinear (vectors share the same direction), and to find unknown points in shapes given known position vectors.
Vectors are part of the Pure Maths strand of A Level Maths and underpin Vector Mechanics and Vectors in 3-d in Year 2 for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: vectors $\overrightarrow{AB}$ and $\overrightarrow{BA}$ have opposite signs — direction matters; for parallel vectors, one is a scalar multiple of the other (so $\mathbf{a} = k\mathbf{b}$ for some $k$), but the vectors do NOT need to be unit length; the magnitude is found using Pythagoras on the components, not by adding them; when finding a unit vector in the direction of $\mathbf{a}$, divide $\mathbf{a}$ by its magnitude — do not just take the components.