0580/21 Oct/Nov 2025, Question 24: Position Vectors
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks
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The question, in short
Using vectors a for OA and b for OB, with B on OD, C on AD, BC parallel to OA at one third its length, and M the midpoint of CD, find M's position vector in terms of a and b.
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Solution · 4 marks
- 1BC = 1/3 OA and BC is parallel to OA, so triangle DBC is similar to triangle DOA with scale factor 1/3
- 2DB = 1/3 DO, so OB = 2/3 OD and OD = 3/2 b
- 3DC = 1/3 DA and M is the midpoint of CD, so DM = 1/6 DA = 1/6(a − 3/2 b) = 1/6 a − 1/4 b
- 4OM = OD + DM = 3/2 b + 1/6 a − 1/4 b
- 5= 1/6 a + 5/4 b
Answer1/6 a + 5/4 b
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Also searched as: 0580/21/O/N/25 · 0580_w25_qp_21 · 0580 w25 21 · question 24.
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