In each discussion group, please create a new forum for this discussion topic (if the GTA has not already done so).

An airplane is at a point P. It must go to an airport positioned at point Q where it will land. Air traffic control has directed the pilot to fly a heading defined by a vector V until able to make a 90 degree turn toward the airport. In this problem, airplanes go in straight lines and turn instantaneously. To be clear, the airplane will fly two legs, each perfectly straight lines in 3D, in order to reach the airport. Further, because of the 90 degree turn, the two legs are orthogonal to each other.

In this problem, you must work out the coordinates of the point W where the airplane makes its turn toward the airport Q.

Show how, analytically, one sets up this problem. In particular, give an equation for the point W in terms of the points P and Q and headingvector V.

Slides 6 through 10 in work through a practice example for pointing a camera. Please first discuss/annotate in your own words each step. Then, as a group, propose a numerical change to the example and work through the modified version.