3D Geometry
Distance of a point from a plane
nta_pyq_2023_jan
Grade 12
Question:
Let P be the plane, passing through the point $(1, -1, -5)$ and perpendicular to the line joining the points $(4, 1, -3)$ and $(2, 4, 3)$. Then the distance of P from the point $(3, -2, 2)$ is
Step-by-Step Solution
Key Concept: Normal to plane = direction vector from $(4,1,-3)$ to $(2,4,3)$: $(-2,3,6)$. Write plane equation, compute distance.
Plane: $-2x+3y+6z+35=0$ (or $2x-3y-6z=35$). Distance from $(3,-2,2)$: $\frac{|6+6-12-35|}{7} = \frac{|-35|}{7} = 5$. Answer: (3)
Correct Answer: 5