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0580/22 May/Jun 2024, Question 24: Position Vectors

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 5 marks

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The question, in short

Parallelogram OPQR with vectors a and b; M midpoint of PQ, N divides QR 2:1. Find vector MN, then position vector of S where MN and OR extended meet.

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

Part (a) · 2 marks

Find vector MN in terms of a and/or b, simplest form.

  1. 1→MQ = 1/2 →PQ = 1/2 b
  2. 2→QR = −a, so →QN = 2/3 × (−a) = −2/3 a
  3. 3→MN = →MQ + →QN = 1/2 b − 2/3 a

Answer1/2 b − 2/3 a

Part (b) · 3 marks

Lines MN and OR extended meet at S; find position vector of S in terms of a and/or b, simplest form.

  1. 1→ON = b + 1/3 a (since →RN = 1/3 →RQ = 1/3 a)
  2. 2→OS = b + 1/3 a + t(1/2 b − 2/3 a), with no a-term because S is on OR
  3. 31/3 − 2/3 t = 0 → t = 1/2
  4. 4→OS = b + 1/3 a + 1/4 b − 1/3 a = 5/4 b

Answer5/4 b

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Also searched as: 0580/22/M/J/24 · 0580_s24_qp_22 · 0580 s24 22 · question 24.
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