3D Geometry
Coplanar Lines — Nearest Point
nta_pyq_2023_apr
Grade 12
Question:
$L_1: \frac{x+3}{5}=\frac{y+1}{4}=\frac{z-2}{\alpha}$ and $L_2: 3x+2y+z-2=0=x-3y+2z-13$ coplanar. Point $P(a,b,c)$ on $L_1$ nearest to $Q(-4,-3,2)$. Then $|a|+|b|+|c|$ is equal to
Step-by-Step Solution
Key Concept: Find $\alpha$ for coplanarity. Then minimize distance from $Q$ to $L_1$.
$10$.
Correct Answer: 4