3D Geometry
Three Dimensional Geometry
nta_pyq_2025_jan
Grade 12
Question:
Let a straight line L pass through the point P (2, -1, 3) and be perpendicular to the lines y+1 x-1 2 = 1 = z-3 -2 and x-3 y-2 z+2 1 = 3 = 4 . If the line L intersects the yz-plane at the point Q, then the distance between the points P and Q is :
Step-by-Step Solution
Key Concept: Apply the core result for lines and planes in three dimensions and simplify using the given constraints.
Vector parallel to L (4) ∣^ i ^ j ^ k ∣ ∣ ∣ ^ ^ ^ = ∣2 1 -2 ∣ = 10 i - 10 j + 5k ∣ ∣ ∣1 3 4 ∣ ^ ^ ^ = 5(2 i - 2 j + k) Equation of ' L ' x-2 y+1 z-3 = = = \lambda( say ) 2 -2 1 Let Q(2\lambda + 2, -2\lambda - 1, \lambda + 3) \Rightarrow 2\lambda + 2 = 0 \Rightarrow \lambda = -1 \Rightarrow Q(0, 1, 2) d(P , Q) = 3
Correct Answer: 4