0606/11 Oct/Nov 2025, Question 12: Vector Proofs
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Given position vectors OA = (1, 7), OB = (7, 4) and OC = k(1, 2), with C on line AB, use vectors to find the ratio AC : AB.
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Solution · 6 marks
- 1AB = (7, 4) − (1, 7) = (6, −3)
- 2AC = k(1, 2) − (1, 7) = (k − 1, 2k − 7)
- 3AC parallel to AB: (k − 1)/6 = (2k − 7)/(−3)
- 4−3k + 3 = 12k − 42 ⇒ k = 3
- 5AC = (2, −1) = (1/3)AB
- 6AC : AB = 1 : 3
AnswerAC : AB = 1 : 3
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