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50:Vectors?ChristineCrisp“TeachALevelMaths”
Vol.2:A2CoreModules
ModuleC4Certainimagesand/orphotosonthispresentationarethecopyrightedpropertyofJupiterImagesandarebeingusedwithpermissionunderlicense.Theseimagesand/orphotosmaynotbecopiedordownloadedwithoutpermissionfromJupiterImages
Avectorhasmagnitudeanddirection.Examplesofvectorsareweight,force,velocityandmomentum.DrawingVectorsMagnitudeisshownbythelengthofaline.Directionisshownbyanarrow.Thisvector...iswrittenas
Vectorsareparallelifoneisamultipleoftheother.
PositionVectorsApositionvectorgivesthepositionofapointrelativetotheorigin,O.e.g.Apositionvectorisusuallywrittenwithasingleletter.xx
xxPositionVectorsApositionvectorgivesthepositionofapointrelativetotheorigin,O.e.g.Anarrowisnotusedbutthelettermustbeunderlined.Intypedwork,thesingleletterusedforapositionvectoristypedinboldandnotunderlined.iscalledthecolumnvectororcomponentform.
abIthinkofthisaswalkingalongthevector.TogetfromAtoBwecouldgo fromAtoO:thenfromOtoB:IfAandBhavepositionvectorsaandbrespectively, canbewrittenintermsofaandb.-a
e.g.IfAandBaregivenby expressasacolumnvector.Solution:
Themid-pointofavectorabxIfMisthemid-pointofAB,Thepositionvectorofthemid-pointofisgivenbytheaverageofthepositionvectorsofAandB.
e.g.IfCandDaregivenby expressasacolumnvector.Solution:Ahugeadvantageofvectorsovertrigorcoordinategeometryisthatworkingin3dimensionsisalmostaseasyas2.
SUMMARYApositionvectorgivesthepositionofapointrelativetotheorigin,O.xxThevectorisgivenbybxThemid-pointofisgivenby(theaverage)
ThemagnitudeisgivenbythelengthAB.MagnitudeofaVectore.g.Thevectorso,usingPythagoras’theorem,Thearrowshowsthedirection.T
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