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0580/22 Feb/Mar 2025, Question 15: Magnitude of a Vector

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 7 marks

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The question, in short

Given point A at (−4, 1) and vector BA as column vector (−5, −12), find point B, vector CA with C at (5, −2), and the magnitude of EF where EF = 3BA.

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Part (a) · 2 marks

Find the coordinates of point B given A and the column vector BA.

  1. 1→BA = A − B, so B = A − →BA
  2. 2B = (−4 − (−5), 1 − (−12))
  3. 3B = (1, 13)

Answer(1, 13)

Part (b) · 2 marks

Find the vector CA using the coordinates of C and A.

  1. 1→CA = A − C = (−4 − 5, 1 − (−2))
  2. 2→CA = column vector (−9, 3)

Answercolumn vector (−9, 3)

Part (c) · 3 marks

Given EF = 3BA, find the magnitude of vector EF.

  1. 1|→BA| = √((−5)² + (−12)²) = √169 = 13
  2. 2|→EF| = 3 × 13 = 39

Answer39

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