Vectors: GCSE Maths revision
A vector has magnitude and direction. Column vectors (x, y) add by adding components. In geometry proofs, paths that start and end at the same point are equal.
Adding and multiplying
(3, 1) + (2, −4)
2a means twice as long, same direction. −a is the opposite direction.
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
(4, −1) + (−2, 5)
3(2, −1)
If AB = (5, 2) and BC = (1, −3), find AC.
Common mistakes
- Subtracting components in the wrong order for BA vs AB.
- Treating vectors like lengths only and dropping direction.
Answers and working
Frequently asked questions
What does a vector proof need?
Express paths in terms of given vectors, then show two paths are equal (parallel and same line) or a scalar multiple (parallel).
Learn, try, get feedback, fix the mistake
ReviseEasy covers GCSE Maths, Combined Science, Triple Science, English Language and English Literature — then drills the topics you keep dropping marks on.
Practise more on ReviseEasy →Related revision
More GCSE revision
ReviseEasy is a GCSE revision website, not a Maths-only site. Lessons, quizzes and flashcards are live for Maths, Combined Science, Triple Biology, Chemistry and Physics, English Language and English Literature. History, Geography and languages are next.