Question
A force F = 2 i - j + 5 k is applied at the point A(1, 2, 5). If its moment about the point B(-1, -2, 3) is 16 i - 6 j + 2 k , then what is the value of ?
NDA
Mathematics
Vector Algebra
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. -2
- B. 0
- C. 1
- D. 2
Answer
A. -2
Step-by-step solution
The position vector of the point of application A with respect to point B is r = r _A - r _B. r = (1 - (-1)) i + (2 - (-2)) j + (5 - 3) k = 2 i + 4 j + 2 k The moment of the force about point B is given by M = r F . M = vmatrix i & j & k \\ 2 & 4 & 2 \\ 2 & - & 5 vmatrix M = i (20 + 2 ) - j (10 - 4) + k (-2 - 8) M = (20 + 2 ) i - 6 j - (2 + 8) k It is given that M = 16 i - 6 j + 2 k . Comparing the coefficients of i and k : 20 + 2 = 16 2 = -4 = -2 -2 - 8 = 2 4 = -8 = -2 Both equations yield = -2. Answer: -2
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