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4024/22 Oct/Nov 2025, Question 10: Magnitude of a Vector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 5 marks

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The question, in short

Given column vectors a = (−3, 4) and b = (8, −2), calculate a scalar multiple combination and the magnitude of their sum.

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

Part (a) · 2 marks

Work out 3a − b as a column vector.

  1. 13a = column vector (−9, 12)
  2. 23a − b = (−9 − 8, 12 − (−2)) = column vector (−17, 14)

Answercolumn vector (−17, 14)

Part (b) · 3 marks

Find the magnitude |a + b| of the sum of the two vectors.

  1. 1a + b = (−3 + 8, 4 + (−2)) = column vector (5, 2)
  2. 2|a + b| = √(5² + 2²) = √29
  3. 3= 5.385… ≈ 5.39

Answer5.39 or 5.385

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