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0580/23 Oct/Nov 2025, Question 8: Magnitude of a Vector

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

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The question, in short

Vector DE is given as the column vector (3, −4). Find a scalar multiple, the magnitude, and the coordinates of E given D is (−2, −3).

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Part (a) · 1 mark

Calculate the column vector 5→DE.

  1. 15 × (3, −4) = (15, −20)

Answercolumn vector (15, −20)

Part (b) · 2 marks

Work out the magnitude of the vector →DE.

  1. 1|DE| = √(3² + (−4)²) = √(9 + 16) = √25
  2. 2= 5

Answer5

Part (c) · 2 marks

Using D at (−2, −3), determine the coordinates of point E.

  1. 1To get from D to E, add →DE = (3, −4) to D.
  2. 2x: −2 + 3 = 1 y: −3 + (−4) = −7
  3. 3E = (1, −7)

Answer(1, −7)

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Also searched as: 0580/23/O/N/25 · 0580_w25_qp_23 · 0580 w25 23 · question 8.
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