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4PM1/02R Jun 2022, Question 1: Position Vectors

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 5 marks

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The question, in short

Given position vector of A as 3i − 2j and AB = 6i + 8j, find B's position vector, the length of AB, and a unit vector along AB.

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

Part (a) · 2 marks

Find the position vector of B in simplified i, j form.

  1. 1OB = OA + AB
  2. 2OB = (3i − 2j) + (6i + 8j)
  3. 3OB = 9i + 6j

Answer9i + 6j

Part (b) · 1 mark

Find the magnitude of vector AB.

  1. 1|AB| = √(6² + 8²)
  2. 2= √100 = 10

Answer10

Part (c) · 2 marks

Find a unit vector parallel to AB in terms of i and j.

  1. 1Unit vector = AB ÷ |AB|
  2. 2= (1/10)(6i + 8j)
  3. 3= 0.6i + 0.8j

Answer(1/10)(6i + 8j) = 0.6i + 0.8j

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