3D Geometry
Line-Plane Meeting Point — Parallel Distance
nta_pyq_2023_apr
Grade None
Question:
Line through $P(2,-1,2)$ and $Q(5,3,4)$ meets $x-y+z=4$ at $R$. Distance of $R$ from $x+2y+3z+2=0$ measured $\parallel$ to $\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}$ is
\sqrt{61}
\sqrt{189}
\sqrt{31}
3
Step-by-Step Solution
Key Concept: Parametrize $PQ$: point $(2+3t,-1+4t,2+2t)$. Substitute in plane to find $R$. Then find distance along given direction.
Distance $=3$.
Correct Answer: 4