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0580/23 May/Jun 2025, Question 12: Magnitude of a Vector

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 5 marks

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The question, in short

Vector questions: multiply a column vector by 5, and find the length of vector JK given points H, K and vector HJ.

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Part (a) · 1 mark

Find 5v where v is the column vector (2, −3).

  1. 15v = column vector (5 × 2, 5 × (−3)) = column vector (10, −15)

Answercolumn vector (10, −15)

Part (b) · 4 marks

Given H(−3, 8), K(−4, 0) and HJ→ = (7, −2), find the magnitude |JK→|.

  1. 1J = (−3 + 7, 8 − 2) = (4, 6)
  2. 2→JK = column vector (−4 − 4, 0 − 6) = column vector (−8, −6)
  3. 3|→JK| = √((−8)² + (−6)²) = √(64 + 36) = √100
  4. 4= 10

Answer10

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