3D Geometry
Distance of a point from a plane
nta_pyq_2023_jan
Grade 12
Question:
The distance of the point $(7, -3, -4)$ from the plane passing through the points $(2, -3, 1)$, $(-1, 1, -2)$ and $(3, -4, 2)$ is:
4
5
$5\sqrt{2}$
$4\sqrt{2}$
Step-by-Step Solution
Key Concept: Find equation of plane through three points using determinant form, then use point-to-plane distance formula.
Equation of plane through three points: $x - z - 1 = 0$. Distance of $(7,-3,-4)$ from plane $= \frac{|7+4-1|}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 5\sqrt{2}$. Answer: (3)
Correct Answer: $5\sqrt{2}$