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4PM1/02R Jun 2024, Question 3: Unit Vectors and i, j Components

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks

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The question, in short

Fixed points O, A, B with |OA| = 3√5, AB = i + 3aj and OB = 7i + 2aj, where a > 0. Find a, then a unit vector parallel to OA.

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Part (a) · 4 marks

Use the given vector lengths and components to find the value of a, given a > 0.

  1. 1OA = OB − AB = 7i + 2aj − (i + 3aj) = 6i − aj
  2. 2|OA| = √(6² + a²) = 3√5
  3. 336 + a² = 45, so a² = 9
  4. 4a > 0 gives a = 3

Answera = 3

Part (b) · 2 marks

Using your value of a, find a unit vector in the direction of OA.

  1. 1OA = 6i − 3j
  2. 2Unit vector = OA/|OA| = (6i − 3j)/(3√5)

Answer±(1/(3√5))(6i − 3j)

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