3D Geometry
Mirror Image of Point in a Line
nta_pyq_2024_jan
Grade 12
Question:
If the mirror image of the point $P(3,4,9)$ in the line $\dfrac{x-1}{3}=\dfrac{y+1}{2}=\dfrac{z-2}{1}$ is $(\alpha,\beta,\gamma)$, then $14(\alpha+\beta+\gamma)$ is:
Step-by-Step Solution
Key Concept: Foot of perpendicular from $P(3,4,9)$ to the line: parametrize as $(1+3t,-1+2t,2+t)$. Direction to $P$ is perpendicular to line direction $(3,2,1)$. Solve for $t$, get foot $F$, then mirror image $=2F-P$.
$14(\alpha+\beta+\gamma)=108$.
Correct Answer: 3