GCSE MATHS GUIDE
GCSE Vectors: routes, operations and midpoints
Vectors describe movement with both size and direction. A reliable method is to follow a route carefully and reverse the sign whenever you travel against a vector arrow.
Column vectors
Add or subtract corresponding components. Multiplying by a scalar changes the magnitude, while a negative scalar also reverses the direction.
Route problems
When expressing one vector in terms of others, choose a route from the start point to the finish point and write each leg in order. Travelling backwards along a known vector changes its sign.
Midpoints and parallel vectors
A midpoint splits a vector into two equal parts. Scalar multiples point along parallel lines, which is often the key relationship in GCSE proof-style vector questions.