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0606/12 May/Jun 2026, Question 11: Expressing Vectors in Terms of a and b

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Given position vectors OA = (4, −2) and OB = (−4, 6), with C on AB dividing AC : CB = 3 : 1 and D on OA where CD = (5, −5.5), find OD and λ.

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Part (a) · 5 marks

Find the vector OD using the division of AB and the given vector CD.

  1. 1AB = OB − OA = column vector (−8, 8)
  2. 2OC = OA + (3/4)AB = (4, −2) + (−6, 6) = column vector (−2, 4)
  3. 3OD = OC + CD = (−2, 4) + (5, −5.5)
  4. 4OD = column vector (3, −1.5)

AnswerOD = column vector (3, −1.5)

Part (b) · 1 mark

Use your OD to find the value of λ where OD = λOA.

  1. 1OD = column vector (3, −1.5) = (3/4) × column vector (4, −2)
  2. 2λ = 3/4

Answerλ = 3/4

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Also searched as: 0606/12/M/J/26 · 0606_s26_qp_12 · 0606 s26 12 · question 11.
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