Question: An airport is at the point (200, 10, 0) and an approaching plane is at the point (550, 60, 4). Assume that the xy-plane is horizontal, with the x-axis pointing eastward and the y-axis pointing northward. Also assume that the z-axis is upward and that all distances are measured in kilometers. The plane flies due west at a constant altitude at a speed of 500 km/hr for half an hour. It then descends at 200 km/hr, heading straight for the airport.
(a) Find the velocity vector of the plane while it is flying at constant altitude.
(b) Find the coordinates of the point at which the plane starts to descend.
(c) Find a vector representing the velocity of the plane when it is descending.