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1、VectorAlgebraNotes:AddingVectors&FindingComponentsSection1)DefinitionofVectors:Readsection2.6"SomeVectorAlgebra"(allreferencesaretoHecht2ndedition)Do2-13M,2-71PQuantitiesthatneedtoberepresentedbymagnitude(size)anddirectionarecalled"vectors"(e.g.displacement,velocity,acceleratio
2、nandforce).Inprintedtext,vectorsareusuallyrepresentedbylettersinboldfont(V).Theycanalsoberepresentedwith"tildes","hats"or"arrows"aboveorbelowtheletter;(e.g.,,,,Vor).Inthisdocument,wewilluseexamplesofsomeofthesenotations.Themagnitudeofavectorisusuallyrepresentedbyunboldeditalict
3、ext(e.g.V).Vectorscanberepresentedindiagramsbyarrows.Thelengthofthearrowrepresentsthevector'smagnitude,andthedirectionthearrowpointsrepresentsthevector'sdirection.Usually,thedirectionisexpressedasanangleqtoaknowndirection(e.g.horizontal).Thepositionofthevectoronthepageisirrelev
4、ant(unlessweareconsideringtorque)andsothearrowrepresentingitcanbemovedtoanywhereonthepageandit'sstillthesamevectoraslongasthelengthanddirectiondon'tchange.11Everyvector(inthisexample)canbethoughtofasbeingtheresultantsumofseparatevectorcomponents,eachoneparalleltoeachofthethreec
5、oordinateaxes:x,yandz.Herewewillonlyconsiderthexandycomponents,VxandVy.Rememberthatwhenfindingcomponents,theoriginalvectorisalwaysthehypotenuseofaright-angletriangleandthexandycomponentsmustbehead-to-tail.RememberthatsometimesthesecomponentscanbenegativeasisVyisinthisexample(if
6、wedefine"up"tobe+ve).Don'tforgettonotecarefullywhichangleinyourtriangleyouwilluseinyourtrigonometrycalculation.Section2)Addingvectors:Readsection2.8"ComponentsandVectorAddition"Do2-61P,2-67P,2-83P,2-85P,2-98PMethod1:AddingVectorsGeometricallyThegeometricalmethodofaddingvectorsi
7、smostsuitableforadding2vectors.Intheoryitworkswhenadding3ormorevectorsbutcanbecomemessy.Toaddtwovectorsgeometrically,youmustarrangethearrowsrepresentingthetwovectorssothattheyarejoinedtogether"headtotail",butwithoutchangingtheirlengthsordirections.Thesumor"resultant"ofthetwovec
8、torsisgeneratedbydrawinganarrowthatstartsatthebeginnin
