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4024/12 May/Jun 2022, Question 25: Expressing Vectors in Terms of a and b

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Parallelograms OABC and OPQR with OA = a, OC = c, OA:OP = 1:4 and OC:CR = 2:3. Find OR, CQ, and the area ratio OABC:OPQR.

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Part (a) · 1 mark

Find vector OR in terms of c.

  1. 1OC : CR = 2 : 3, so OR : OC = 5 : 2
  2. 2→OR = (5/2)c

Answer(5/2)c

Part (b) · 2 marks

Find vector CQ in terms of a and c, simplified.

  1. 1→CR = (3/2)c and →RQ = →OP = 4a
  2. 2→CQ = →CR + →RQ
  3. 3= 4a + (3/2)c

Answer4a + (3/2)c or (8a + 3c)/2

Part (c) · 1 mark

Find the ratio of the area of OABC to the area of OPQR.

  1. 1OP = 4 × OA and OR = (5/2) × OC, with the same angle at O
  2. 2Area OPQR = 4 × 5/2 × area OABC = 10 × area OABC
  3. 3Area OABC : area OPQR = 1 : 10

Answer1 : 10

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Also searched as: 4024/12/M/J/22 · 4024_s22_qp_12 · 4024 s22 12 · question 25.
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