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4PM1/02 Nov 2023, Question 11: Vector Geometry

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 9 marks

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The question, in short

Using vectors OA = 4p + 5q, OB = 3p + q and OC = 2p − 4q with M the midpoint of OC, work out a vector expression and a ratio involving collinear points.

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

Part (a) · 3 marks

Express the vector MA in terms of p and q in its simplest form.

  1. 1OM = (1/2)OC = p − 2q
  2. 2MA = −OM + OA
  3. 3= −(p − 2q) + (4p + 5q) = 3p + 7q

AnswerMA = 3p + 7q

Part (b) · 6 marks

Given N on OB with M, N and A collinear, determine the ratio MN : NA.

  1. 1MN = λ(3p + 7q)
  2. 2MN = MO + ON = −(p − 2q) + μ(3p + q)
  3. 3Compare p: 3λ = −1 + 3μ; compare q: 7λ = 2 + μ
  4. 4Solve: 18λ = 7, λ = 7/18 (μ = 13/18)
  5. 5MN : NA = 7 : 11

AnswerMN : NA = 7 : 11

Stuck on a step? Read the free lesson: Vector Geometry

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