Question
Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0. Question: What is the equation of the line L ?
NDA
Mathematics
Three Dimensional Geometry
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 1-x=y+2=3-z
- B. -(x+1)=y-2=z+3
- C. 3x+3=2y-4=6z+18
- D. 3x-3=2y+4=6z-18
Answer
C. 3x+3=2y-4=6z+18
Step-by-step solution
The line L is perpendicular to the plane 2x+3y+z+5=0, so its direction ratios are proportional to the normal vector of the plane, which is (2, 3, 1). The equation of the line passing through (-1, 2, -3) with direction ratios (2, 3, 1) is given by: x+1 2 = y-2 3 = z+3 1 Multiplying the entire equation by 6, we get: 3(x+1) = 2(y-2) = 6(z+3) 3x+3 = 2y-4 = 6z+18 Answer: 3x+3=2y-4=6z+18
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks