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4024/13 May/Jun 2026, Question 23: Vector Geometry

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Triangle OAB has vector OA = 3a and vector OB = b. Find vector AB, then vector OX where X divides AB with AX : XB = 2 : 3.

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Part (a) · 1 mark

Express vector AB in terms of a and b.

  1. 1→AB = →AO + →OB
  2. 2= −3a + b = b − 3a

Answerb − 3a

Part (b) · 3 marks

Given AX : XB = 2 : 3 on AB, find vector OX in terms of a and b in simplest form.

  1. 1→AX = 2/5 →AB = 2/5(b − 3a)
  2. 2→OX = →OA + →AX = 3a + 2/5 b − 6/5 a
  3. 3= 9/5 a + 2/5 b

Answer9/5 a + 2/5 b or 1/5(9a + 2b)

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Also searched as: 4024/13/M/J/26 · 4024_s26_qp_13 · 4024 s26 13 · question 23.
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