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1、高等数学(下册)(Highermathematics(inChinese))Similartotheplaneanalyticgeometry,analyticgeometryisbycoordinatemethod,thespatialpointandthreeorderedrealnumber,spacepatternandestablishedtherelationshipwiththethreeelementequation,geometricproblemscanusealgebraicm
2、ethodstostudyspace.Spaceanalyticgeometryknowledgeastheknowledgeoftheplaneanalyticgeometryisanimportantfoundationforlearningaunaryfunctioncalculus,calculusisessentiallearningmultiplefunctionsofknowledge.Inthischapter,firstlydiscussthespacerectangularcoo
3、rdinatesystem,iswidelyusedandtheconceptofvectoroperationbasedonengineeringtechnology,andthentothevectorasatooltodiscusstheplanespaceinastraightline,curvedsurfaceandcurvesomeoftheequationsandtheircontents.8.1spacerectangularcoordinatesystem8.1.1spacerec
4、tangularcoordinatesystemInthespaceofaselectedpointO,Oforthreeperpendicularaxes,bothofthemtakeOastheoriginandgenerallyhavethesamelength.ThisthreeaxesarecalledX(horizontal)axisandtheYaxis(verticalaxis)andZaxis(verticalaxis);referredtoascoordinateaxes.Usu
5、allytheXaxisandtheYaxisconfigurationinthehorizontalplane,andtheZaxisistheplumbline;thepositivedirectiontheyshouldcomplywiththeruleofrighthand,therighthandholdingtheZaxis,whiletherighthandfourfingersfromthepositivexaxistoPI2angletothepositiveYaxis,Zaxis
6、ispositivetothethumb,sothreetheaxisiscomposedofarectangularspacecoordinatesystem,Oiscalledtheoriginofcoordinates(Figure8and1).Thethreeaxesofanytwocandetermineaplane,sothatthethreeplanesreferredtocoordinateplane.XaxisandYaxisofcoordinateplaneisknownasxO
7、y,theothertwocoordinateplaneisyOzandzOx.Thethreecoordinateplanesofthespaceisdividedintoeightparts,eachpartcalledbythethreeoctant.Positivehalfaxisdefinitionoftheoctantiscalledthefirstoctant,itislocatedinthetopxOy.InthexOyabovethecounterclockwisearrangem
8、entofthesecondquadrantandthirdquadrantandfourthquadrantxOy.Inthelowerpart,andthefirstoctantcorrespondingtothefifthoctants.Counterclockwiseinarrangementofthesixthoctants,seventhoctantsandthegossiplimit.Eightoctantsarerepresentedbythelett