Grade 12 Calculus and Vectors: Unit 6 - Geometric Vectors
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Course
Vectors
Institution
12th Grade
Grade 12 Calculus and Vectors Unit 6 Notes on Geometric Vectors. Include topics varying from scalars, vectors, true bearings, quadrant bearings, triangle law of addition, parallelogram law of addition, vector properties, vector properties for scalar multiplication, linear combination of vectors, eq...
6I
Ascalar is a quantitythathasamagnitudeonly opirection
Ii In
value ieskano
numerical metres
is by
described
updownleft
Avectoris a quantitythathas and
magnitude direction
SCALAR VECTOR
Distance 40metres is
Displacement distance in a
speed 40kminr velocity is speedin aspecific
direction nokmin Nw
µ weight is the forcedownwards
dueto gravity saznewtons
directedline segment
Avectoris described graphically as a orRay
vectorscanbenamedeither by
o usingtheendpoints
of
or as a single letter representation
I
Themagnitude of a vector describesits size or lengthand is representedby it orlats
lats or is always positive a negative descriptionvalveindicates a changein directionto the description direction
vie aforceisactingleftwithmagnitude an thisimplies itis actinginthedirectiontotherightwithtruemagnitude an
as describedearlier direction istypically described as updownleftright or relativeto other known positions Thereare tw
standard descriptions mostcommonlyused
atrueBearing
thisdescribes a direction by
i
127
the northas areferencestart
using
andmeasuresclockwise tothefinalposition
2 QuadrantBearing a
this describes a directionbyusingthe
compassaxisas thereferenceand rotating we sa se
go
seeties
atmostgodegreesfromtheaxis
is
1 Equivalentvectorsarevectors thathave
equalmagnitude a
osamedirection of Be
o B
2 oppositevectorsare vectorsthathave an c
requal magnitude
OF cis
o B
, 3Parallel vectors are vectorsthathave
equaloropposite direction
notnecessarily thesamemagnitude
I there is nosuchthing as subtractingvectors youalwaysaddtheoppositeor negativevector
2 vectorsare alwaysaddedheadtotail
a e f
s a the produced or resultantrectorwilljointhetailof
g p a
a thefirsttothehead ofthesecond
ate is calledthe resultantvector
the equivariantvectoristherectorthatproduces a o vector denoted aso if the resultantvectorisnotthe zerovectorthenthe
nt isthe vectorthatisoppositetheresultantvector
equilibria
O hasno direction and no magnitude
e
a thisarrangementproducesthezerovectorandcreates
a 25 cats
n whatiscalled a stateof equilibrium
thesesetsofvectorsareall in a state of equilibriumNomatterwhereyoustartinthediagramthevectorsareconnectedinsuchaway
that theycycleback tothestartingpoint
s e a e
e a
r
Two methods of aDoinavectors
1 Triangle Lawof addition
i 5 i s
wesimplyaddvectorsby tailtotailand
vectors are positioned
transposingthemtoconnect the parallelogram is formedwiththe
head to tail parallelvectorsthediagonalisthe
resultantas snownconnectingtailtail
to headhead
a ate 5
itis
Q ABCDis a parallelogram
noteBcandDcareninesegmentsandnotrayscreators inthe diagram
maranerogram
a law pete
a
atriangle
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