3D Geometry
Foot of Perpendicular from Point to Line
nta_pyq_2024_jan
Grade 12
Question:
Let $(\alpha,\beta,\gamma)$ be the foot of perpendicular from the point $(1,2,3)$ on the line $\dfrac{x+3}{5}=\dfrac{y-1}{2}=\dfrac{z+4}{3}$. Then $19(\alpha+\beta+\gamma)$ is equal to:
Step-by-Step Solution
Key Concept: Parametrize: $(5t-3,2t+1,3t-4)$. Direction to $(1,2,3)$ perpendicular to $(5,2,3)$: $(1-5t+3)5+(2-2t-1)2+(3-3t+4)3=0$. Solve for $t$.
$19(\alpha+\beta+\gamma)=101$.
Correct Answer: 2