3D Geometry
Distance from Point to Plane Parallel to Line
nta_pyq_2023_apr
Grade 12
Question:
Plane $P$ contains $2x+y-z-3=0=5x-3y+4z+9$ and is parallel to $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Distance of $A(8,-1,-19)$ from $P$ measured $\parallel$ to $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$ is equal to _________
Step-by-Step Solution
Key Concept: Find plane $P$ using intersection of two given planes and parallel condition. Then find intersection of line through $A$ (parallel direction) with $P$, compute distance.
$26$.
Correct Answer: 26