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4MA1/2H Jun 2024, Question 24: Vector Geometry

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Quadrilateral OACB has OA = 4a, OB = 3b and BC = 2a + b; find vector AC, then use a vector method with P on AC and straight lines OPQ, BCQ to find OQ.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Find vector AC in terms of a and b, giving the simplest form.

  1. 1AC = AO + OB + BC
  2. 2AO = −4a
  3. 3OB = 3b
  4. 4BC = 2a + b
  5. 5−4a + 3b + 2a + b = −2a + 4b
  6. 64b − 2a

Answer4b − 2a

Part (b) · 4 marks

Given AP : PC = 3 : 2 and OPQ, BCQ straight, find vector OQ in terms of a and b by a vector method, showing working.

  1. 1AC = −2a + 4b, so AP = 3/5 AC = −6/5 a + 12/5 b.
  2. 2OP = OA + AP = 14/5 a + 12/5 b.
  3. 3Q on OP: OQ = λ(14/5 a + 12/5 b). Q on BC: OQ = 3b + μ(2a + b).
  4. 4Match a: 14λ/5 = 2μ. Match b: 12λ/5 = 3 + μ. So λ = 3.
  5. 5OQ = 3(14/5 a + 12/5 b) = 8.4a + 7.2b

Answer8.4a + 7.2b

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