- 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.
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.
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.