0580/21 May/Jun 2022, Question 26: Position Vectors
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks
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The question, in short
Using vectors a for OA and b for OB, with K dividing AB in ratio 1:2 and OALK a parallelogram, work out L's position vector in terms of a and b, simplified.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1→AB = b − a, so →AK = 1/3(b − a)
- 2→OK = a + 1/3(b − a) = 2/3 a + 1/3 b
- 3OALK is a parallelogram, so →AL = →OK
- 4→OL = a + 2/3 a + 1/3 b = 5/3 a + 1/3 b
Answer5/3 a + 1/3 b
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Also searched as: 0580/21/M/J/22 · 0580_s22_qp_21 · 0580 s22 21 · question 26.
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