As you approach the space station, three beacons on the nearest face (at the
corners of the triangle marked in white) transmit their coordinates to you:
beacon 1: .60929i + 2.00000j + 2.76202k
beacon 2: -.46707i + 4.00000j + 4.44768k
beacon 3: -.46707i + 2.00000j + 4.44768k
Wanting to keep track of how far away your shuttle is from the front plane of the space station you have coded a computer program which takes the positions of the beacons and the shuttle's position and returns the distance to the closest point on the nearest plane. At the instance the shuttle passes through the point:
shuttle: 2.900337i + 4.00000j + 4.22495k
what distance will the program register?
Determine the coordinates of the nearest point on the station and check that the line from this point to the shuttle is perpendicular.