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0606/13 May/Jun 2025, Question 10: Vector Geometry

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Using vectors a and b from O to A and B, with A, B, C collinear and AB/AC = 1/3, express OC and then use a point D beyond A and point E on CD to find λ.

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Part (a) · 3 marks

Express the vector OC in terms of a and b, giving it in simplified form.

  1. 1AB = b − a
  2. 2AC = 3AB = 3(b − a)
  3. 3OC = a + 3(b − a) = 3b − 2a

AnswerOC = 3b − 2a

Part (b) · 5 marks

With OA : AD = 2 : 7 and E on CD where OE = λb, determine the numerical value of λ.

  1. 1OD = OA + AD = a + (7/2)a = 4.5a
  2. 2DC = OC − OD = 3b − 2a − 4.5a = 3b − 6.5a
  3. 3OE = OD + μDC = 4.5a + μ(3b − 6.5a)
  4. 4a: 4.5 − 6.5μ = 0, so μ = 9/13
  5. 5b: λ = 3μ = 27/13

Answerλ = 27/13

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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 10.
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