3D Geometry
Plane Rotation — Distance from Rotated Plane
nta_pyq_2023_apr
Grade 12
Question:
Plane $4x-y+z=10$ rotated by $\frac{\pi}{2}$ about its intersection with $x+y-z=4$. $\alpha$ = distance of $(2,3,-4)$ from new plane. $35\alpha$ is equal to
Step-by-Step Solution
Key Concept: New plane: family $(4x-y+z-10)+\lambda(x+y-z-4)=0$. After $90°$ rotation, new plane $\perp$ original. Normal dot original normal $=0$.
$35\alpha=126$.
Correct Answer: 3