Transcription of THREE–DIMENSIONAL GEOMETRY - Number theory
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THREE–DIMENSIONAL GEOMETRY - Number theory
Chapter 8 three IntroductionIn this chapter we present a vector algebra approach to three dimensionalgeometry. The aim is to present standard properties of linesand planes,with minimum use of complicated three dimensional diagrams such as thoseinvolving similar triangles. We summarize the chapter:Pointsare defined as ordered triples of real numbers and thedistancebetween pointsP1= (x1, y1, z1) andP2= (x2, y2, z2) is defined by theformulaP1P2=p(x2 x1)2+ (y2 y1)2+ (z2 z1) line segments-ABare introduced as three dimensional columnvectors: IfA= (x1, y1, z1) andB= (x2, y2, z2), then-AB= x2 x1y2 y1z2 z1 .IfPis a point, we letP=-OPand callPtheposition suitable definitions oflines,parallel lines, there are important ge-ometrical interpretations of equality, addition and scalar multiplication ofvectors.
Chapter 8 THREE–DIMENSIONAL GEOMETRY 8.1 Introduction In this chapter we present a vector–algebra approach to three–dimensional geometry. …
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