After being bored in your previous calculus class (and definitely not in multivariable calculus) you count the floor tiles to see how large the room is. You now know that the room is 32 feet wide and 42 feet in length. Additionally, your tall friend Chuck can barely jump and touch the ceiling which means the ceiling is 10 feet high. Your calculus professor notices you doing these measurements and decides to create a classroom coordinate system. Your professor walks to the center of the room and notices that their head is five feet above the ground and sets their head as the origin of the classroom coordinate system. Your friend Alice is sitting at \(A = (9, -6, -2.5)\text{,}\) a projector is located at position \(B = (0,1,3)\text{,}\) and your friend Carlos is working while sitting on the floor at \(C = (-2, 20, -5)\text{.}\) All distances are measured in feet.
