Mapping Data Center Cable Routes in Three Dimensions

You work as a junior technician for a company that maintains a multi-floor data center. The building has three floors, and your team needs to plan cable routes and network equipment placement using a 3D coordinate system. The origin is at the northwest corner of the ground floor, with the [latex]x[/latex]-axis pointing east, the [latex]y[/latex]-axis pointing south, and the [latex]z[/latex]-axis pointing up (all measurements in meters).

Your supervisor has given you a facilities map with coordinates for server racks, network switches, and cable entry points. You need to write equations for straight cable runs between equipment, calculate distances to verify cable length requirements, and determine the angles between equipment planes to ensure proper ventilation spacing. This planning work ensures the data center runs efficiently—supporting everything from online classes to hospital records to small business websites that people from all walks of life depend on every day.