资源描述：
《vector analysis - welcome to university of malaya向量分析-欢迎来到马来亚大学》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、VectorAnalysisSummaryofprerequisites(revision)1.Ascalarquantityhasmagnitudeonly;avectorquantityhasbothmagnitudeanddirection.2.Theaxesofreference,OX,OY,OZ,formaright-handedset.Thesymbolsi,j,kdenoteunitvectorsinthedirectionsofOX,OY,OZ,respectively.Ifthen3.Thedirectioncosinesaretheco
2、sinesoftheanglesbetweenthevectorrandtheaxesOX,OY,OZ,respectively.Foranyvectorr=axi+ayj+azk4.ScalarProduct(DotProduct)whereistheanglebetweenAandB.IfA=axi+ayj+azkandB=bxi+byj+bzkthen5.Vectorproduct(CrossProduct)AxB=C=ABsinθn;nisaunitvectorinadirectionperpendiculartoAandB6.Anglebetwe
3、entwovectorsForperpendicularvectorsForparallelvectorsSolve!:a)IfPisthepoint(3,2,6),determiner,,l,m,andnb)IfA=2i+3j+4kandB=i-2j+3k,findthedirectioncosinesofeachvectorhencetheanglebetweenAandBc)IfA=2i-3j+4kandB=i+2j+5k,determineandverifyd)IfA=3i-2j+4kandB=2i-3j-5k,determineandverify
4、Answers:a)b)c)d)TripleProductofthreevectorsIfThenRememberingthatWehaveExample:IfPropertiesofscalartripleproducta)Sinceinterchangingtworowsinadeterminantreversesthesign.Itcanbeshowni.ethescalartripleproductisunchangedbyacyclicchangeofthevectorsinvolved.b)i.eachangeofvectorsnotincyc
5、licorder,changesthesignofthescalartripleproductc)sincetworowsareidenticalisavectorproductofBandC,ofmagnitudeactinginadirectionperpendiculartotheplaneofBandCandformingaright-handedsetCoplanarvectorsIf,IfAisathirdvectorperpendicularto,thenA,BandCarecoplanarif:Vectortripleproductsoft
6、hreevectors:IfTakenotethatItcanbeprovedthat:Example:IfEquivalentlyusingTrythese:Determinefora)Answer:b)Answer:DifferentiationofvectorsManypracticalproblemsdealwithvectorsthatchangewithtime(independentscalar)e.g.velocity,accelerationetc.IfAcanberepresentedasDifferentiatingwithrespe
7、cttotIngeneralifuistheindependentscalarparameterExample:Aparticlemovesinspacesothatattimetitspositionisstatedby:Findthecomponentsofitsvelocityandaccelerationinthedirectionofthevectorwhent=1Att=1AunitvectorparalleltoThecomponentof(velocity)inthedirectionof:Thecomponentof(accelerati
8、on)inthedirectionof:Differentiati
