Vector Geometry
GCSE and IGCSE geometry support for vectors and geometric proofs.
Describing movement and proof with vectors
A vector has both magnitude and direction. In GCSE Higher and IGCSE geometry, vectors describe translations, routes and relationships in shapes. The glossary entry for a vector provides useful vocabulary before proof questions.
Key knowledge and step-by-step method
Add vectors by adding corresponding components. Subtract by reversing the second vector, and multiply by a scalar by multiplying every component. In diagrams, choose a route from the starting point to the finishing point and add the labelled vectors in order. Equivalent routes must produce equal expressions.
Worked examples
Example 1: (3, 2) + (1, -5) = (4, -3). Example 2: 2(4, -1) = (8, -2). Example 3: If AB = a and BC = b, then AC = a + b. If another route from A to C gives 2c, then a + b = 2c.
Common mistakes and exam advice
Keep direction consistent, use negative signs when travelling against an arrow, and state the final conclusion in proof questions. A vector expression alone may not explain why lines are parallel or points are collinear.
Practice exercises and answers
Exercise 1: Add (2, 7) and (-5, 1). Answer: (-3, 8). Exercise 2: Calculate 3(-2, 4). Answer: (-6, 12). Exercise 3: OA = p and AB = 2q. Find OB. Answer: OB = p + 2q.
Related learning across the website
Continue through Geometry Lessons, Algebra Lessons, straight-line graphs, transformations, translations, enlargements, rotations, reflections, gradient and trigonometry lessons
Benefits of one-to-one maths tutoring
One-to-one lessons with maths tutor Ryan Harvey can improve notation, route selection and proof language through personalised diagrams and immediate feedback.
Contact and lesson enquiry
Students and parents can contact MasterMaths Tutoring for personalised vector support.