# 233PRINT-print - Definition Let n be a positive integer...

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DefinitionLetnbe a positive integer. Then theCartesian productofncopies of the real number lineRis:Rn=R×R×. . .×R={(a1,a2, . . . ,an)|ajR},which is the set of all orderedn-tuples of real numbers.Example(a)R2=R×R={(a1,a2)|aiR}is the Euclidean plane.(b)R3=R×R×R={(a1,a2,a3)|aiR}is Euclidianthree-space.
ExampleWhat surfaces inR3are represented by the following equations?(a)z= 3(b)y= 5Solution
ExampleDescribe and sketch the surface inR3represented by theequationy=x.
Distance Formula in Three DimensionsThe distance|P1P2|between the pointsP1(x1,y1,z1) andP2(x2,y2,z2) is|P1P2|=p(x2-x1)2+ (y2-y1)2+ (z2-z1)2.
|P1P2|