0606/11 May/Jun 2026, Question 11: Vector Geometry
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 8 marks
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The question, in short
Triangle OAB has OA = a, OB = b. X on OA with OA = 3OX, Y on XB with XB = 5XY, Z on OB with OB = mOZ, and OX = nZY. Use vectors to find m and n.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 8 marks
- 1OX = (1/3)a and XB = b − (1/3)a
- 2XY = (1/5)(b − (1/3)a) = (1/5)b − (1/15)a
- 3OZ = (1/m)b
- 4ZY = −(1/m)b + (1/3)a + (1/5)b − (1/15)a = (4/15)a + (1/5 − 1/m)b
- 5(1/3)a = n((4/15)a + (1/5 − 1/m)b)
- 6a: 1/3 = 4n/15, so n = 5/4
- 7b: 0 = 1/5 − 1/m, so m = 5
Answerm = 5, n = 5/4
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