This key facts covers Key Results to Remember within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 10 of 12 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Key Results to Remember
- Midpoint: OM = ½(OA + OB) — always the average of the two position vectors.
- Parallel test: p parallel to q if and only if p = kq (k is a non-zero scalar).
- Collinear test: Parallel vectors + common point = collinear points.
- Ratio m:n: fraction of the way along = m/(m+n).
- Direction only: two vectors being parallel says nothing about their position — always note the shared point when proving collinearity.
Practice questions for Vectors (Geometry Proofs)
Vector AB goes from point A to point B. Which of the following describes vector BA?
A student says: 'I have shown that vector AB is parallel to vector CD, so A, B, C, D all lie on the same straight line.' Explain why the student's reasoning is incorrect.
Quick recall flashcards
When are two vectors parallel?
Two vectors p and q are parallel when one is a scalar multiple of the other: p = kq for some non-zero scalar k. They point in the same or exactly opposite direction.
If AB = a, what is BA?
BA = -a. Reversing the direction of travel negates the vector. In diagrams: if you travel against an arrow, write a negative sign in front of that vector.