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4024/13 May/Jun 2025, Question 12: Position Vectors

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Vector PQ is (4, −2). With Q at (2, 5), find P's position vector, and find a given the length of PQ equals √a.

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Part (a) · 2 marks

Given the position vector of Q is (2, 5), work out the position vector of P.

  1. 1→OP = →OQ − →PQ
  2. 2= (2, 5) − (4, −2) = (2 − 4, 5 + 2)
  3. 3Position vector of P = column vector (−2, 7)

Answercolumn vector (−2, 7)

Part (b) · 2 marks

Using the vector PQ, find the value of a such that the magnitude of PQ is √a.

  1. 1|→PQ|² = 4² + (−2)² = 16 + 4 = 20
  2. 2|→PQ| = √20, so a = 20

Answer20

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