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4024/12 May/Jun 2026, Question 20: Position Vectors

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

In triangle OPQ with O as origin, R lies on OQ and OQ = 3OR, with vector OP = 3a and vector OR = 2b; X is midpoint of PQ. Find vectors in terms of a and b.

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Part (a) · 1 mark

Find vector PR in terms of a and b, simplified.

  1. 1→PR = →PO + →OR
  2. 2= −3a + 2b

Answer2b − 3a

Part (b) · 1 mark

Find vector RQ in terms of a and b, simplified.

  1. 1→OQ = 3 × 2b = 6b
  2. 2→RQ = 6b − 2b = 4b

Answer4b

Part (c) · 3 marks

Find the position vector of X in terms of a and b, simplified.

  1. 1→PQ = −3a + 6b
  2. 2→PX = 1/2 →PQ = 3b − 3/2 a
  3. 3→OX = 3a + 3b − 3/2 a
  4. 4= 3/2 a + 3b

Answer3/2 a + 3b or (3a + 6b)/2 or 3/2(a + 2b)

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Also searched as: 4024/12/M/J/26 · 4024_s26_qp_12 · 4024 s26 12 · question 20.
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