Lemmara logoLemmaraWorked solution

4024/13 May/Jun 2025, Question 24: Vector Geometry

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Quadrilateral OACB has vectors OA = a and OB = b, with AC parallel to OB and AC = 2OB. Express given vectors in terms of a and b.

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

Part (ai) · 1 mark

Write the vector from A to B using a and b.

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

Answerb − a

Part (aii) · 1 mark

Write the vector from O to C using a and b.

  1. 1→AC = 2→OB = 2b
  2. 2→OC = →OA + →AC = a + 2b

Answera + 2b

Part (b) · 3 marks

Point X lies on OC with OX : XC = 4 : 1. Express the vector from B to X in terms of a and b.

  1. 1→OX = 4/5 →OC = 4/5(a + 2b)
  2. 2→BX = →BO + →OX = −b + 4/5 a + 8/5 b
  3. 3= 4/5 a + 3/5 b

Answer4/5 a + 3/5 b or (4a + 3b)/5

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

Practise more vector geometry questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on vector geometry

Also searched as: 4024/13/M/J/25 · 4024_s25_qp_13 · 4024 s25 13 · question 24.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.