Students should have completed Section 1.3: Vector Products and should be familiar with equations for lines in space before starting this discussion. However, they should not have read Section 1.4: Lines and Planes. The discussion should be preceded by a brief lecture on planes including the different ways to characterize a plane geometrically and the vector description of planes which comes from Exercise 2 of Discussion 4.
In each exercise students are asked to determine an equation which must be satisfied by all points in the plane given different information about the plane. In the first exercise they begin with a point in the plane and a line perpendicular to the plane. In the second exercise they begin with the vector description of the plane, that is, a point and two vectors which lie in the plane. Finally in the third exercise they begin with three non-collinear points which lie in the plane. Students will probably need to complete the write-up of this discussion outside of class.