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4MA1/1H Jun 2025, Question 23: Vector Geometry

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Triangle OAB with P midpoint of OA, Q on OB, lines ABR and PQR straight. Given OA = 12a and OB = 8b, find vector AB and then n where OQ = nb.

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

Part (a) · 1 mark

Express the vector AB in terms of a and b.

  1. 1→AB = →AO + →OB
  2. 2= −12a + 8b

Answer−12a + 8b

Part (b) · 4 marks

Using AB : BR = 1 : 2 and a vector method, find the value of n where OQ = nb.

  1. 1→AR = 3→AB = −36a + 24b
  2. 2→PR = →PA + →AR = 6a + (−36a + 24b) = −30a + 24b
  3. 3→PQ = →PO + →OQ = −6a + nb
  4. 4P, Q, R collinear: −6a + nb = λ(−30a + 24b)
  5. 5a: −6 = −30λ, so λ = 1/5
  6. 6b: n = 24 × 1/5 = 24/5 = 4.8

Answer4.8

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