3D Geometry
Image of Point in Plane — Sum of Coordinates
nta_pyq_2023_apr
Grade 12
Question:
Plane $P$ through $\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}$ and $(2,4,-3)$. Image of $(-1,3,4)$ in $P$ is $(\alpha,\beta,\gamma)$. Then $\alpha+\beta+\gamma$ is equal to
Step-by-Step Solution
Key Concept: Find plane $P$: normal = (line direction) $\times$ (vector from line point to $(2,4,-3)$). Reflect $(-1,3,4)$ in $P$.
$\alpha+\beta+\gamma=10$.
Correct Answer: 1