0580/42 Feb/Mar 2025, Question 21: Position Vectors
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks
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The question, in short
Triangle OAB has C midpoint of OA, with vector OC = m and vector CB = n. Point E divides AB in ratio AE:EB = 4:5. Find the position vector of E in terms of m and n, simplified.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1→OA = 2m and →OB = →OC + →CB = m + n
- 2→AB = →OB − →OA = n − m
- 3→AE = 4/9 →AB = 4/9(n − m)
- 4→OE = 2m + 4/9(n − m)
- 5= (14/9)m + (4/9)n
Answer(14/9)m + (4/9)n
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