4MA1/1H Jan 2022, Question 22: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Triangle OAB with OA→ = 8a, OB→ = 6b, M on OB with OM:MB = 1:2, N midpoint of AB, P where ON and AM meet. Use vectors to find OP→ in terms of a and b.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1ON = OA + ½AB = 8a + ½(6b − 8a) = 4a + 3b
- 2AM = AO + OM = −8a + 2b
- 3OP = μ(4a + 3b) and OP = 8a + λ(−8a + 2b) = (8 − 8λ)a + 2λb
- 4Equate: 4μ = 8 − 8λ and 3μ = 2λ, so 16μ = 8 and μ = 0.5
- 5OP = 0.5(4a + 3b) = 2a + 1.5b
Answer2a + 1.5b
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