MTH 310 Chapter Notes - Chapter 10_2: Parallelogram, Ofu-Olosega, Horse Length
18 Jan 2020
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A nd ib c avectoriv indicates aquantitythathasbothmagnitudeanddirectionlegdisplacementvelocityforceetc oftenrepresentedyb anarrow aparticlemovesfrompointatopointb thedisplacementvector hasaninitialpointaandaterminalpointb indicatedas v abs ifavectoruhasthesamemagnitudeanddirectionthen uanduareequivalentrequalvectors indicatedbya v thezerovectorhaslengthof0andistheonlyrectorwithnospecificdirection denotedby0 combiningvectors if aparticlemovesfromatob abandthenmovesfrombto lcbtthenat bt at. Atiscalledthesum ofabandbi re a is n vectoraddition if uandu arevectorspositionedsothattheinitialpointofv is atterminalpointofu thensumu v isthevectorfromtheinitialpointof u totheterminalpointofv scalarmultiplication if eis ascalarandv is avectorthenthescalarmultiple cv is a vectorwhoselengthis. 14timesthelengthofv whosedirectionisthesameas v if c 0andoppositeif 40 if c o orv othencu 0 scalarmultiplesareparallel if avectorhasthesamemagnitudebutoppositedirectionsuchas idv v thenit iscalledthenegativeofv ntrianglelaw parallelogramlaw. Ex2 if a andb arethevectorsshowndraw a 2b n a b o aab n a m. 2b a components if weplacetheinitialpointofvectora attheoriginofarectangularcoordinatesystemthenwecanrepresentthevector withcoordinatescalledthecomponentsof a writtenas a la ad or a la a a equivalentvectorsatdifferentpositionsontheplanearecalled representations ofthe algebraicvector the representation of 01tfromtheorigintopointp13. 2isthe positionvectorofpointp tofindthepositionvectorwithpointsarky 7 andbix y 2. At f 2 2 i 3 i 4 l4,4 3 themagnitudeorlengthofvectorv is thelengthofanyofitsrepresentationsandis denotedby thesymbol ivl orhullandis calculatedas.
