3D Geometry
Image of Point in Line — Distance from Second Line
nta_pyq_2026_jan
Grade 12
Question:
Let $Q(a,b,c)$ be the image of the point $P(3,2,1)$ in the line $\dfrac{x-1}{1}=\dfrac{y}{2}=\dfrac{z-1}{1}$. Then the distance of $Q$ from the line $\dfrac{x-9}{3}=\dfrac{y-9}{1}=\dfrac{z-5}{-2}$ is
Step-by-Step Solution
Key Concept: Foot of perpendicular from $P(3,2,1)$ to line: $F=(2,2,2)$ (by projection). $Q=2F-P=(1,2,3)$.
Distance $=7$.
Correct Answer: 3