Vector Proofs: The Logic Engine
Edexcel 4MA1 • 5.1 G • Parallel & Collinear Vectors
Parallel Vector Detection
The Logic Track
Parallel Vector Test:
Two vectors are parallel if one is a scalar multiple of the other.
u = k × v
Method: Can you factorize one to look like the other?
If YES → Parallel
If NO → Not Parallel
Collinearity Test:
Three points A, B, C are collinear if:
1. They share a common point
2. The vectors connecting them are parallel
AB parallel to BC + Point B is shared = Collinear
EXAMINER TRAP:
❌ Just saying "the vectors are parallel" is NOT enough!
✓ You MUST state:
1. The vectors are parallel (with proof)
2. The common point they share
Both conditions = Full marks!
Bridge Strategy:
Phase 1 - Anchor:
Start with simple positive multiples. Build confidence with clear examples like 2, 3, 4...
Dynamic Solver: Proof Builder
Question:
Prove that points A, B, and C are collinear if:
AB = 1a + 2b
AC = 3a + 6b
AC = 3a + 6b
AC = 3(1a + 2b)
AC = 3 × AB
We can write: AC = 3 × AB
This shows AC is a scalar multiple of AB
Since AC = 3 × AB,
Therefore, vectors AB and AC are parallel.
Point A is common to both vectors AB and AC.
Since:
1. AB and AC are parallel, AND
2. Point A is common to both vectors,
Therefore, points A, B, and C are collinear.
✓ Show factorization clearly
✓ State that vectors are parallel
✓ Identify the common point
✓ Write a conclusion using "collinear"
Missing ANY of these = Lost marks!
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