3D Geometry
Intersecting Lines — Minimum Value of 8αβ
nta_pyq_2023_apr
Grade 12
Question:
If $\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}$ and $\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}$ intersect, then magnitude of minimum value of $8\alpha\beta$ is _____
Step-by-Step Solution
Key Concept: Intersecting lines: coplanarity condition gives relation between $\alpha$ and $\beta$. Minimize $|8\alpha\beta|$ using AM-GM.
Minimum $|8\alpha\beta|=18$.
Correct Answer: 18