4024/12 May/Jun 2024, Question 25: Expressing Vectors in Terms of a and b
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Using vectors a for OA and b for OB in triangle OCB, with A dividing OC in ratio 1:3 and X the midpoint of BC, express the position vector of X in terms of a and b.
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Solution · 3 marks
- 1OA : AC = 1 : 3, so →OC = 4a
- 2X is the midpoint of BC: →OX = 1/2(→OB + →OC)
- 3→OX = 1/2(b + 4a) = 2a + (1/2)b
Answer2a + (1/2)b
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Also searched as: 4024/12/M/J/24 · 4024_s24_qp_12 · 4024 s24 12 · question 25.
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