3D Geometry
Foot of Perpendicular on Line of Intersection
nta_pyq_2023_apr
Grade 12
Question:
$P_1:\ 3x-y-7z=11$; $P_2$ through $(2,-1,0),(2,0,-1),(5,1,1)$. Foot of perpendicular from $(7,4,-1)$ on $P_1\cap P_2$ is $(\alpha,\beta,\gamma)$. Then $\alpha+\beta+\gamma$ is equal to
Step-by-Step Solution
Key Concept: Find direction of $P_1\cap P_2$ = $\vec{n}_1\times\vec{n}_2$. Parametrize line, find foot.
$\alpha+\beta+\gamma=11$.
Correct Answer: 11