4MA1/2H Jun 2022, Question 21: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Triangle OAB has OA = 4a and OB = 6b, with Q on AB and OQP a straight line, AP = 2a + 8b. Use vectors to find the ratio AQ : QB.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1OP = OA + AP = 4a + 2a + 8b = 6a + 8b
- 2AB = −4a + 6b; let AQ = t × AB, so OQ = (4 − 4t)a + 6tb
- 3OQ is a multiple of OP, so (4 − 4t) : 6t = 6 : 8
- 48(4 − 4t) = 36t, so 32 = 68t and t = 8/17
- 5AQ = 8/17 of AB, so AQ : QB = 8 : 9
Answer8 : 9
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