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4024/11 May/Jun 2024, Question 24: Expressing Vectors in Terms of a and b

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Quadrilateral ABCD has midpoints H, K, L, M on AB, BC, CD, AD; with AB = 2a, BC = 2b, AD = 2d, find vectors HK, CD and ML in terms of a, b, d.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Find vector HK in terms of a and b.

  1. 1HK = HB + BK = 1/2(2a) + 1/2(2b)
  2. 2HK = a + b

Answera + b

Part (b) · 1 mark

Find vector CD in terms of a, b and d.

  1. 1CD = CB + BA + AD = −2b − 2a + 2d
  2. 2CD = −2a − 2b + 2d

Answer−2a − 2b + 2d or 2(d − a − b)

Part (c) · 2 marks

Find vector ML in terms of a, b and d.

  1. 1ML = MD + DL = d + 1/2 DC
  2. 2DC = 2a + 2b − 2d, so 1/2 DC = a + b − d
  3. 3ML = d + a + b − d = a + b

Answera + b

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Also searched as: 4024/11/M/J/24 · 4024_s24_qp_11 · 4024 s24 11 · question 24.
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