0580/22 May/Jun 2025, Question 23: Vector Geometry
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 3 marks
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The question, in short
Using vectors a for OA and b for OB, with BC parallel to OA and three times its length, and M the midpoint of AC, work out M's position vector in simplest form from a and b.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1→AC = →AO + →OB + →BC = −a + b + 3a = 2a + b
- 2→AM = 1/2 →AC = a + (1/2)b
- 3→OM = →OA + →AM = a + a + (1/2)b
- 4= 2a + (1/2)b
Answer2a + (1/2)b
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Also searched as: 0580/22/M/J/25 · 0580_s25_qp_22 · 0580 s25 22 · question 23.
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