4MA1/1H Jan 2023, Question 24: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Using vectors with OA = 2a, OB = 2b and DE = 7a + 3b, and AB : BD = 1 : 2, find the ratio OC : CE given that O, C, E are collinear.
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Solution · 5 marks
- 1AB = 2b − 2a, so BD = 2(2b − 2a) and OD = 2b + 4b − 4a = 6b − 4a
- 2OE = OD + DE = 6b − 4a + 7a + 3b = 3a + 9b
- 3C on OE: OC = λ(3a + 9b). C on AB: OC = 2a + μ(2b − 2a)
- 4Compare: 3λ = 2 − 2μ and 9λ = 2μ, so 12λ = 2 and λ = 1/6
- 5OC = (1/6) OE, so CE = (5/6) OE and OC : CE = 1 : 5
Answer1 : 5
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