Autonomous Drone Flight Path Separation (Aerospace & Computer Engineering)

Two autonomous package delivery drones navigate a shared urban airspace corridor. Radar telemetry tracks their straight-line 3D flight paths:

• Drone 1 ($L_1$): Flies through waypoint $P(2, 0, 1)$ along direction $\vec{v}_1 = \langle 1, 2, -1 \rangle$.
• Drone 2 ($L_2$): Flies through waypoint $Q(1, 3, 2)$ along direction $\vec{v}_2 = \langle 2, -1, 1 \rangle$. (All coordinates and velocity rates are normalized in meters).

FAA and UNLV autonomous systems safety protocols mandate an emergency avoidance maneuver if the minimum clearance distance between two flight corridors is less than $2.0\text{ meters}$.

1. Write the vector and parametric equations for both flight paths using independent parameters $t$ (Drone 1) and $s$ (Drone 2).
2. Classify the spatial relationship between $L_1$ and $L_2$ (Parallel, Intersecting, Skew, or Coincident).
3. Compute the shortest perpendicular distance between point $P(2, 0, 1)$ on Drone 1's corridor and the straight flight path $L_2$ using the point-to-line clearance formula.
4. Determine whether Drone 1's waypoint violates the $2.0\text{ m}$ safety clearance envelope.