CHAPTER 12 MISCELLANEOUS 3D PROBLEMS

This chapter includes a variety of problems involving 3D lines, planes, tetrahedra, and 3D circles. Most of these are commonly (or at least occasionally) encountered problems, while others, although less commonly encountered, serve to show how various techniques may be brought to bear on new problems.

12.1 PROJECTION OF A POINT ONTO A PLANE

In this section, we consider the projection of a point Q onto a plane P, where P is defined as ax + by + cz + d = 0 (or image), as shown in Figure 12.1. By definition, the line segment between Q and its projection Q’ is parallel to the plane normal . Let the (signed) distance ...

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