MTH 310 Chapter 10_1: 10.1 Three-Dimensional Coordinate System
18 Jan 2020
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Three dimensional coordinatesystem torepresentpointsinspacethereisanoriginthroughwhichthecoordinateaxespassthexaxistheyaxisandthezaxis xandyaxesarehorizontal zaxisisvertical zn z x u y righthandruledeterminesthedirectionof aaxis y x u ifyoucurltheringersofyourrighthandaroundthezaxisinthedirection ofa900counterclockwise rotationfromthe positive xaxistopositiveyaxisthenyourthumbpointsinthepositivedirectionofthezaxis theaxesdeterminethecoordinateplanes thexyplanetheyzplaneandthereplane theplanesdividespaceintoeightpartsoctantswiththefirstoctantbeingdeterminedbythepositiveaxes r ya n n xy. P if pis a pointinspacethe a bandc arethecoordinatesof p a isthex coordinateb istheycoordinateandc isthe2 coordinate r p lab c. S lao c x pointp determines a rectangularbox: y if alineisdroppedfrompointpto aplanethepointonthatplaneistheprojectionofponthexyip. hrplane. Rsisthecartesianproductrxrxr ixydlx yze r representingallorderedtriplesofrealnumbers bygivingaonetoone correspondencebetweenpointspandorderedtriplesrabc in1313 athreedimensionalrectangular coordinatesystem anequationinxyand2 representsa surfacein1123i in xandy represents a curvein k. Ex1 whatsurfacesin1133arerepresentedbythe followingequations y s a 2 3 al z 3 representstheset x y riz33orallpointsin rwi z 3 thisisa horizontalplanethatisparallelto y srepresentstheset x y zly s orallpointsinkswly sthisis averticalplaneparalleltothe n planean the xyplaneandis3unitsaboveit is 5unitstotherightof it. Ex2 describeandsketchthesurfacein ksrepresentedbyy x y x representstheset x x zl xc r ze r thisis a verticalplanethatintersectsthexyplane at y x 2 0. 1ppal x x i ly y i iz 2,7. Ex4 findanequation of a spherewithradiusr andcenter4h k l distance fromc.
