0580/23 Oct/Nov 2024, Question 26: Vector Geometry
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks
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The question, in short
Using vectors a and b for OA and OB, with AK:KB = 2:1 and OK = KC, find vector AC in terms of a and b in simplest form.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1→AB = −a + b, so →AK = 2/3(−a + b)
- 2→OK = a + 2/3(−a + b) = 1/3 a + 2/3 b
- 3OK = KC, so →OC = 2 × →OK = 2/3 a + 4/3 b
- 4→AC = −a + 2/3 a + 4/3 b = −1/3 a + 4/3 b
Answer−1/3 a + 4/3 b
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Also searched as: 0580/23/O/N/24 · 0580_w24_qp_23 · 0580 w24 23 · question 26.
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