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4024/11 Oct/Nov 2023, Question 23: Position Vectors

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Parallelogram OABC has OA = a and OC = c; X is midpoint of AC, Y divides AB with AY:YB = 2:1. Find vectors AC, OX and YX in terms of a and c.

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

Part (a) · 1 mark

Write vector AC in terms of a and c.

  1. 1→AC = →AO + →OC = −a + c
  2. 2= c − a

Answerc − a

Part (b) · 2 marks

Find the position vector of X, the midpoint of AC, in terms of a and c.

  1. 1→OX = →OA + 1/2 →AC = a + 1/2(c − a)
  2. 2= 1/2 a + 1/2 c

Answer1/2 a + 1/2 c

Part (c) · 2 marks

Find vector YX in terms of a and c, using Y on AB with AY:YB = 2:1.

  1. 1→AB = →OC = c, so →AY = 2/3 c
  2. 2→YX = →YA + →AX = −2/3 c + 1/2(c − a)
  3. 3= −1/2 a − 1/6 c

Answer−1/2 a − 1/6 c

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Also searched as: 4024/11/O/N/23 · 4024_w23_qp_11 · 4024 w23 11 · question 23.
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