4: Vector Geometry
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- 4.1: Vectors and Lines
- 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 to describe rotations, reflections, and projections of the plane R2. We now apply the same techniques to 3-space to examine similar transformations of \RR3. Moreover, the method enables us to completely describe all lines and planes in space.
- 4.2: Projections and Planes
- Any student of geometry soon realizes that the notion of perpendicular lines is fundamental.