0580/22 Oct/Nov 2023, Question 26: Vector Geometry
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks
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The question, in short
In parallelogram OPQT with position vectors a for P and b for T, K divides PQ in ratio 3:1; lines OK and TQ extended meet at X. Find X's position vector in terms of a and b, simplest form.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1→PQ = b, so →OK = a + 3/4 b
- 2X lies on OK extended and on TQ (height b): →OX = λ(a + 3/4 b) with 3/4 λ = 1
- 3λ = 4/3, so →OX = 4/3 a + b
- 4Position vector of X = b + (4/3)a
Answerb + (4/3)a
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Also searched as: 0580/22/O/N/23 · 0580_w23_qp_22 · 0580 w23 22 · question 26.
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