4MA1/1HR Jan 2022, Question 24: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Trapezium OXYZ has vectors OX = a, XY = b, OZ = 3b, M midpoint of OX, N where MNZ and ONY are straight. Given ON:OY = λ:1, use vectors to find λ.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1ON = λOY = λ(a + b)
- 2MN = MO + ON = −½a + λ(a + b) = (λ − ½)a + λb
- 3MZ = −½a + 3b, and MN is parallel to MZ, so MN = μ(−½a + 3b)
- 4Compare: λ = 3μ and λ − ½ = −½μ, so 3.5μ = ½ and μ = 1/7
- 5λ = 3 × 1/7 = 3/7
Answer3/7
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