4PM1/01 Jun 2023, Question 10: Unit Vectors and i, j Components
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 10 marks
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The question, in short
Given fixed points O, A, B with OA = (b + 1)i + bj and AB = 3i, and unit vector along OB = (√17/34)[(3a + 2)i + bj], find exact a and b, where a, b > 0.
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Solution · 10 marks
- 1AB = OB − OA = [(3a + 2) − (b + 1)]i = 3i, so 3a − b = 2, b = 3a − 2
- 2√17/34 = 1/√68, so |OB| = √68: (3a + 2)² + b² = 68
- 3(3a + 2)² + (3a − 2)² = 68, so 18a² + 8 = 68
- 4a² = 10/3, a = √30/3 (a > 0)
- 5b = 3(√30/3) − 2 = √30 − 2
Answer(i) a = √30/3 (ii) b = √30 − 2
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