This key facts covers Vector Notation Recap 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 3 of 12 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Vector Notation Recap
- Column vector: written as a column, e.g. the vector 3 right and 2 up is (3, 2) written vertically.
- Bold letters: in textbooks, vectors are written in bold: a, b. In handwriting, underline them: a, b.
- Arrow notation: vector from A to B is written as AB with an arrow above. AB = OB - OA (position of end minus position of start).
- Negative vector: BA = -AB (the same distance, opposite direction).
- Scalar multiple: 2a is a vector twice as long as a in the same direction. -3a is three times as long in the opposite direction.
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
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.
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.