1.1-1.2 vector and space coordinates

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1、VectorandVectorSpaceChapter1magnituderelation—Part1vectoralgebraPart2SpaceanalyticgeometryInthreedimesionalspace:Spaceform—point,line,surfaceBasicmethod—coordinate;vectorcoordinate,EquationsystemSpaceanalyticgeometryandvectoralgebraThischapterintroducesthefundamentalconceptsofvectoralgebraandanal

2、yticgeometryinspace.Theseconceptsareveryinmportantnotonlyforstudyingthecalculusoffunctionsofseveralvariablesinthenextbook,butalsoforuseinapplicationsinphysics,mechanics,othersciences,andengnieering.2.linearoperationofvectors3.spacerectangularcoordinatessystem4.linearoperationofvectorbyusingcoordi

3、nate5.moduleanddirectioncosineofvector1.1-1.21.theconceptofvectorzero（nonzero/unit）vector零（非零/单位）向量initialpoint起点terminalpoint终点adirectedlinesegment有向线段Parallelorcollinearvectors平行/共线向量orthogonal/perpendicular正交/垂直co-plane共面parallelogram/trianglelaw平行四边形/三角形法则rectangularcoordinatesysteminspace空间直

4、角坐标系Theright-handrule右手规则octant卦限Coordinatedecompositionofvector向量的坐标分解式Moduli模Directioncosineofvector向量的方向余弦I、InductionTwokindsofquantities:Scalar:mass,area,temperature…Vector:force,displacement,velocity…II、GeometricdiscriptionofvectorsanditsoperationsDefinition1Ifaquantityhasbothmagnitudeanddir

5、ection,wecallitvector.Denotedby1.Notes:Thearrowsymbol“→”shouldn’tbeomitted.Avectorisoftenrepresentedbyanarrowofadirectedlinesegment.Thelengthofthearrowrepresentsthemagnitude/module/normofthevector(denotedby)andthearrowpointsinthedirectionofthevector.III.SomespecialvectorsFreevectors：Avectorisdete

6、rminedcompletelybyitslengthanddirectionandisindependentofthelocationofitsinitialpointandtermiminalpoint,wecallitasfreevector.Remark:Allfreevectorscanbemovedtothesameinitialpoint.Definition2Twovectorsarecalledbythesamevectors,iftheyhavethesamedirectionandthesamelength,denotedby.Definition3zerovect

7、orisavectorwhichhasthesameinitialandterminalpoint.It’sdirectionisarbitrary.Definition4Avectoriscalledzerovectorifthelengthofitis0,itcanbewrittenbyDefinition5Avectoriscalledanunitvector,ifthelengthofitis1.1.Everydirecti