Aerospace Engineering & Air Traffic Control (Flight Path Conflict)

Two commercial aircraft are flying linear routes within an airport's terminal radar control area. Their paths relative to the control tower origin (measured in kilometers) are modeled parametrically as:

• Flight A: $x = 2 + 2t, \quad y = 7t, \quad z = 3 + 5t$
• Flight B: $x = -3 + 2s, \quad y = -1 + 6s, \quad z = 4 + 5s$

1. Analyze the direction vectors to determine if the flight trajectories are parallel.
2. Determine if the flight paths are intersecting or skew to assess if there is a spatial collision hazard.