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0580/42 Feb/Mar 2024, Question 7: Vector Geometry

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

Vector questions: scale a column vector, subtract two column vectors, find the magnitude of the difference, then use a triangle with MS:SN = 5:3 to find the position vector of S.

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

Part (ai) · 1 mark

Given q = (−4, 5), find 3q as a column vector.

  1. 13q = 3 × (−4, 5)
  2. 2= column vector (−12, 15)

Answercolumn vector (−12, 15)

Part (aiia) · 1 mark

Given p = (8, −5) and q = (−4, 5), find p − q.

  1. 1p − q = (8 − (−4), −5 − 5)
  2. 2= column vector (12, −10)

Answercolumn vector (12, −10)

Part (aiib) · 2 marks

Find the magnitude |p − q| of the vector from part (ii)(a).

  1. 1|p − q| = √(12² + (−10)²) = √244
  2. 2= 15.62… ≈ 15.6

Answer15.6 or 15.62…

Part (b) · 3 marks

In triangle OMN with →OM = a, →ON = b and MS : SN = 5 : 3, find the position vector of S in terms of a and b, simplified.

  1. 1MN = b − a
  2. 2MS = 5/8 (b − a)
  3. 3OS = a + 5/8(b − a)
  4. 4= 3/8 a + 5/8 b

Answer3/8 a + 5/8 b

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