Discussion 4: Using the Language of Vectors

The goal of this discussion is for the students to develop an understanding of how to give vector descriptions of subsets of the plane and of space. This discussion is designed to be used after the students have been introduced to the basic terminology and algebra of vectors. In particular, students should have seen vector addition and scalar multiplication and the correspondence between vectors and points in the plane or in space.

The first exercise asks the students to describe in words and to sketch subsets of the plane and space which are one dimensional. The second exercise considers subsets of space which are two dimensional. In each case, the exercises again require that students are able to interpret set notation. The ideas presented here are used in Section 1.4: Lines and Planes in giving vector descriptions of lines and planes and in the introduction to Discussion 5 on planes. Students should be able to complete this discussion in a single period and put their solutions on the board at the end of class.