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1、3VECTORSANDCOORDINATESYSTEMSConceptualQuestions3.1.Themagnitudeofthedisplacementvectoristheminimumdistancetraveledsincethedisplacementisthevectorsumofanumberofindividualmovements.Thus,itisnotpossibleforthemagnitudeofthedisplacementvectortobemorethanthedistancetraveled.
2、Iftheindividualmovementsareallinthesamedirection,thetotaldisplacementandthedistancetraveledareequal.However,itispossiblethatthetotaldisplacementislessthanthedistancetraveled,iftheindividualmovementsarenotinthesamedirection.dd3.2.ItispossiblethatCAB=+onlyifAandBbothpoin
3、tinthesamedirectionasinthefigurebelow.ItisnotddpossiblethatCAB>+because,ifAandBpointindifferentdirections,puttingthemtiptotailgivesaresultantwithashorterlength(seefigurebelow).dd3.3.ItispossiblethatC=0ifAB=−.Itisnotpossibleforthelengthofavectortobenegative,soC≥0.Evenif
4、dddAandBareparallelbutinoppositedirections,Cwillstillhavealengthgreaterthanorequaltozero.3.4.No,itisnotpossibletoaddascalartoavector,sincethescalarhasnodirection.d3.5.Thezerovector0haszerolength.Itdoesnotpointinanydirection.3.6.Avectorcanhaveacomponentthatiszeroandstil
5、lhavenonzerolengthonlyifanothercomponentisnonzero.Forexample,considerthevectoriˆ=(1,0),whichpointsalongthex-axis.3.7.Ifonecomponentofavectorisnonzerothenitisnotpossibleforthevectortohavezeromagnitude.Themagnitudeofthevectordependsonthesumofthesquaresofthecomponents,soa
6、nycomponentsignsdonotmatter.3.8.No,itisnotpossiblefortwovectorswithunequalmagnitudestoaddtozero.Toaddtozero,twovectorsmustbeantiparallelandofthesamelength(magnitude).©Copyright2013PearsonEducation,Inc.Allrightsreserved.Thismaterialisprotectedunderallcopyrightlawsasthey
7、currentlyexist.Noportionofthismaterialmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.3-13-2Chapter33.9.(a)False,becausethesizeofavectorisfixed.(b)False,becausethedirectionofavectorinspaceisindependentofanycoordinatesystem.(c)True,becau
8、setheorientationofthevectorrelativetotheaxescanbedifferent.ExercisesandProblemsSection3.1VectorsSection3.2Propertieso
