0606/13 May/Jun 2026, Question 10: Vector Proofs
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Parallelogram OABC has OA = a and OB = b. D is on OB with OD : OB = 1 : 3, E is on AC with AE : AC = 2 : 3. Show DE is parallel to AB.
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Solution · 5 marks
- 1AB = OB − OA = b − a
- 2OD = (1/3)b; OC = AB = b − a, so AC = b − a − a = b − 2a
- 3OE = a + (2/3)(b − 2a) = (2/3)b − (1/3)a
- 4DE = OE − OD = (2/3)b − (1/3)a − (1/3)b
- 5DE = (1/3)(b − a) = (1/3)AB, so DE is parallel to AB
AnswerDE = (1/3)(b − a) = (1/3)AB, so DE is parallel to AB shown
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