Chapter 8 Analytic Geometry in Three-Dimensional Space
In two-dimensional analytic geometry, equations represent curves on a plane. In three-dimensional space, equations represent geometric objects such as planes and lines. This chapter builds a complete toolkit for describing and analyzing these objects algebraically and geometrically.
We will organize the chapter into four sections:
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Planes and their equations.
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Lines and their equations.
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Position relations among lines and planes.
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Angles and distance formulas in space.
A major learning goal is to move fluently between geometric language (normal vectors, directions, intersections) and equation language. We will use many figures to make every formula geometrically meaningful.
