Computer Graphics & Game Engines (Ray-Traced Laser Sight)

In a 3D video game engine, a player fires a sniper rifle that projects a straight laser-sight line through space. Concurrently, a thin vertical power cylinder on the map is modeled as a line segment. The game engine maps out the equations of these two lines in local coordinate space as:

• Laser Sight Line ($L_1$): $x = t, \quad y = 2 - t, \quad z = 3 + 2t$
• Power Cylinder Axis ($L_2$): $x = 2 + s, \quad y = s, \quad z = 7 + s$

1. Classify the geometric relationship between the laser sight line and the cylinder axis line (equal, parallel, intersecting, or skew).
2. If the lines intersect, determine the exact 3D coordinates $(x, y, z)$ where the laser beam strikes the cylinder.