4.0: Prelude to Vector Geometry

In this chapter we study the geometry of 3-dimensional space. We view a point in 3-space as an arrow from the origin to that point. Doing so provides a “picture” of the point that is truly worth a thousand words. We used this idea earlier, in Section 2.6, to describe rotations, reflections, and projections of the plane \(\mathbb{R}^2\). We now apply the same techniques to 3-space to examine similar transformations of \(\mathbb{R}^3\). Moreover, the method enables us to completely describe all lines and planes in space.

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