christine crisp每本级数学卷核心模块向量个.pptx

50:Vectors?ChristineCrisp“TeachALevelMaths”

Vol.2:A2CoreModules

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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