4MA1/1H Jun 2021, Question 26: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
In trapezium OACB, OA→ = 2a, OB→ = 5b and AC→ = 3b, with AC parallel to OB. Diagonals OC and AB meet at P. Find OP→ in terms of a and b, showing working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1OC = OA + AC = 2a + 3b, and P is on OC, so OP = n(2a + 3b)
- 2AB = AO + OB = −2a + 5b, and P is on AB, so OP = 2a + m(−2a + 5b)
- 3Matching the a terms: 2n = 2 − 2m
- 4Matching the b terms: 3n = 5m
- 5From the second, m = 3n/5; putting that in the first gives 2n = 2 − 6n/5
- 610n = 10 − 6n, so 16n = 10 and n = 5/8
- 7OP = (5/8)(2a + 3b) = (5/4)a + (15/8)b
Answer(5/4)a + (15/8)b
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