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← All visuals GCSE Higher Maths (Grades 5–9)

2D column vectors & geometric vector proofs

Start with Column vectors on a grid (adding, subtracting and scaling m a + n b), or switch to Geometric proofs (parallel & collinear) to build route vectors step by step through midpoints and ratio points.

Screen:
Proof diagram:
Tap route steps below or drag ratio point P Parallel: MN = ½ AB
Interactive route builder & ratio controls

1. Step-by-step route vectors

Collect like terms in a and b

2. Factorising & proving parallel / collinear

GCSE exam conclusion

Two non-zero vectors u and v are parallel if and only if one is a scalar multiple of the other (v = k u). Three points are collinear if the vectors between them are parallel and share a common point.