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4024/22 May/Jun 2023, Question 10: Magnitude of a Vector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Given points F(6, 1) and G(−2, 4) with vector GH = (−1, −8), find the length of FH; then use a quadrilateral diagram with OA = a, OB = b, AC = kb and X on OC to work with vectors.

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

Part (a) · 3 marks

Work out the magnitude of the vector from F to H.

  1. 1H = G + GH = (−2 − 1, 4 − 8) = (−3, −4)
  2. 2FH = (−3 − 6, −4 − 1) = (−9, −5)
  3. 3|FH| = √((−9)² + (−5)²) = √106
  4. 4= 10.29… ≈ 10.3

Answer10.3 or 10.29 to 10.30

Part (bi) · 2 marks

Express the vector OX using m, k, a and b.

  1. 1OC = OA + AC = a + kb
  2. 2OX = m(a + kb) = ma + mkb

Answerm(a + kb) or ma + mkb

Part (bii) · 3 marks

Given BX = 3/5 a − 1/2 b, determine k.

  1. 1BX = BO + OX = −b + ma + mkb
  2. 2Compare with 3/5 a − 1/2 b: m = 3/5
  3. 3mk − 1 = −1/2, so mk = 1/2
  4. 4k = (1/2) ÷ (3/5) = 5/6

Answer5/6

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Also searched as: 4024/22/M/J/23 · 4024_s23_qp_22 · 4024 s23 22 · question 10.
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