Question
The position vectors of three points A, B and C are a , b and c respectively such that 3 a - 4 b + c = 0 . What is AB : BC equal to?
NDA
Mathematics
Vector Algebra
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 3:1
- B. 1:3
- C. 3:4
- D. 1:4
Answer
B. 1:3
Step-by-step solution
Given 3 a - 4 b + c = 0 Rearranging the terms: 3 a - 3 b = b - c -3( b - a ) = -( c - b ) Using the definition of position vectors, AB = b - a and BC = c - b : -3 AB = - BC BC = 3 AB Taking the magnitude on both sides: | BC | = 3| AB | BC = 3AB AB BC = 1 3 Thus, AB : BC = 1 : 3. Answer: 1:3
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