GCSE-readyVectors
A vector has size and direction. Vectors describe movement and help prove geometric facts.
Column vectors
(3 over −2) means 3 right and 2 down.
Add by adding the tops and the bottoms. Multiply every part by a number to scale it.
2 × (1 over 4) = (2 over 8)
Add by adding the tops and the bottoms. Multiply every part by a number to scale it.
2 × (1 over 4) = (2 over 8)
Vector paths
To get from A to C, go A → B → C: AC = AB + BC.
Going backwards changes the sign: BA = −AB.
Going backwards changes the sign: BA = −AB.
Parallel vectors (Higher)
Vectors are parallel if one is a multiple of the other. 2a + 4b = 2(a + 2b), so it is parallel to a + 2b.
If AB and BC are parallel and share point B, then A, B and C are collinear (in a straight line).
If AB and BC are parallel and share point B, then A, B and C are collinear (in a straight line).
a = (2 over 1) and b = (−1 over 3). Find 2a + b.
- 2a = (4 over 2)
- 2a + b = (4 + −1 over 2 + 3)
Answer: (3 over 5)
Add and scale column vectors part by part. AC = AB + BC; BA = −AB. Parallel vectors are multiples of each other.
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