3D Geometry
Three Dimensional Geometry
nta_pyq_2025_jan
Grade 12
Question:
The perpendicular distance, of the line y+2 x-1 2 = -1 = z+3 2 from the point P(2, -10, 1) , is :
6
5\sqrt2
4\sqrt3
3\sqrt5
Step-by-Step Solution
Key Concept: Apply the core result for lines and planes in three dimensions and simplify using the given constraints.
(4) x - 1 y + 2 z + 3 = = = \lambda (let ) 2 -1 2 (2\lambda + 1, -\lambda - 2, 2\lambda - 3) - -\to \to ∵ PA ⋅ n = 0 \Rightarrow (2\lambda - 1)2 + (-\lambda + 8)(-1) + (2\lambda - 4)2 = 0 \Rightarrow 4\lambda - 2 + \lambda - 8 + 4\lambda - 8 = 0 \Rightarrow 9\lambda - 18 = 0 \Rightarrow \lambda = 2 \therefore A(5, -4, 1) 2 2 2 \therefore AP = \sqrt3 + 6 + 0 = \sqrt45 = 3\sqrt5
Correct Answer: 4