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4MA1/2HR Jun 2025, Question 18: Expressing Vectors in Terms of a and b

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks

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The question, in short

In triangle OAB, OA→ = 4a and OB→ = 4b, with P on AB where AP : PB = 1 : 3. Find AB→ and OP→ in terms of a and b.

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Part (a) · 1 mark

Write down the vector AB→ in terms of a and b.

  1. 1AB→ = AO→ + OB→
  2. 2= −4a + 4b

Answer−4a + 4b

Part (b) · 2 marks

Express the vector OP→ in terms of a and b, giving the simplest form.

  1. 1AP = 1/4 of AB
  2. 2OP→ = OA→ + 1/4 AB→
  3. 3= 4a + 1/4(−4a + 4b)
  4. 4= 4a − a + b
  5. 5= 3a + b

Answer3a + b

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