4MA1/1H Jan 2021, Question 23: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
Triangle OAB has OA→ = 2a and OB→ = 2b, with M the midpoint of AB and N on OB where ON : NB = 2 : 1. Using vectors, find the ratio OP : PM, where P lies on AN and OPM is straight.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1OM = OA + ½AB = 2a + (b − a) = a + b
- 2AN = ON − OA = (4/3)b − 2a
- 3OP = OA + λAN = (2 − 2λ)a + (4λ/3)b, and also OP = k(a + b)
- 4Equate: 2 − 2λ = 4λ/3, so λ = 3/5 and k = 4/5
- 5OP = (4/5)OM, so OP : PM = 4 : 1
Answer4 : 1
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