LectureNotes
1 2 dimensionalrepresentation
oxryaxis
x ycoordinates
wecallthisp laneinthesetofrealnumbers
with2coordinates
called172because apointcanbewritten
2 3 dimensional representation R
x.y.azaxis
xy zcoordinates
1stoctantx.y.azare allpositive
bestwaytodrawthecoordinateplane
someb asicquestionsgetdifficulttoanswer
on
1 theangleyoulookatthegraph
everythingdependson
Points
wecan'taddsubtractmultiplyordividepoints
Youcanmeasuredistancebetweentwopoints
thedistancebetweentwo Remember
pointsin R is pa coxy on
in thedistancebetweentwopointsis
PQ 107 0 7 COZY
tect.fi
n
iiiiIii
Aspherecenteredat10,31
radiuss
Whatdoes 2 427216describein I der
the fnf
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10.2.07
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cylinderis
Eh ofthis
EEEreal
,the
In If jointsthatare5unitsawayfrom10,31
Thecylinderexample
thesetofallpointsthatare 4unitsawayfromaxis ER
12.2Vectorsin are
ifhEff
t.it
ment
faint
c mgare mesegment
operationsonvectors
If
HEmustbefloatingtodo
this
EE fItEIw̅
on
mIiE
n.IE n
2AlgebraicAspect
A ordered ofrealnumbers
t riplet
T.IT
Iff
scala
acx.cy.cz
I ÉÉÉ
men
,Lecture3 8130
Leftoverwednesdaymaterial
wecandefinem agnitudelengthofavectorv
cabs data inR2
a bc datba.ca inR
if I811 thenitiscalledaunitvector
ex calculate andidentifyunitvectors
magnitude
I t.LI r cunitvectors
Incantuan
aFor
what 4,123 aunitvector
scalarkisKxc
14212232 1169 13 K
butalsoitcouldbe becauseitwould
stillbeaunitvector
anyvector ifwedivideitbyitsownmagnitudewegetaunitvectorinthedirectionofit
For
notappearinthetextbook
5specialunitvectors
ifanyvectorit isalreadya
so caned unitvectorthenP I
2 0,17 called
Anyrectorvcanbeexpressed
a10,0 caned as asumofscalarmultiplesof I
aitbitck
Section12.3Dot
P roduct
9 1 1289Iforn wewanttodefinea numerical
quantity that thelenghtsofbothvectorstogetherwithameasurementoft heirrelative
combines
alignment
be ex factor
itrowpointinthesamedirectionalignmentfactor
should
waggement
YfYaymenago In Han
b
, if0istheanglebetweenvowwhentheyaredrawnatthes amestartingpoint
thencos0isthedesiredalignment
Yo i Ew̅ 181181coso
consequences
1 JPIEPsoIPINET
2 ifv18 Fw̅ 0
components Projection
igna
wing
fcomprwl .ro
ftp.fome.fi tiff
jojrw
compit w̅ I
projuw̅ w̅ i i
1 2 dimensionalrepresentation
oxryaxis
x ycoordinates
wecallthisp laneinthesetofrealnumbers
with2coordinates
called172because apointcanbewritten
2 3 dimensional representation R
x.y.azaxis
xy zcoordinates
1stoctantx.y.azare allpositive
bestwaytodrawthecoordinateplane
someb asicquestionsgetdifficulttoanswer
on
1 theangleyoulookatthegraph
everythingdependson
Points
wecan'taddsubtractmultiplyordividepoints
Youcanmeasuredistancebetweentwopoints
thedistancebetweentwo Remember
pointsin R is pa coxy on
in thedistancebetweentwopointsis
PQ 107 0 7 COZY
tect.fi
n
iiiiIii
Aspherecenteredat10,31
radiuss
Whatdoes 2 427216describein I der
the fnf
ftp.affffgfferefd
10.2.07
i
i go.org
ffffffI4h
cylinderis
Eh ofthis
EEEreal
,the
In If jointsthatare5unitsawayfrom10,31
Thecylinderexample
thesetofallpointsthatare 4unitsawayfromaxis ER
12.2Vectorsin are
ifhEff
t.it
ment
faint
c mgare mesegment
operationsonvectors
If
HEmustbefloatingtodo
this
EE fItEIw̅
on
mIiE
n.IE n
2AlgebraicAspect
A ordered ofrealnumbers
t riplet
T.IT
Iff
scala
acx.cy.cz
I ÉÉÉ
men
,Lecture3 8130
Leftoverwednesdaymaterial
wecandefinem agnitudelengthofavectorv
cabs data inR2
a bc datba.ca inR
if I811 thenitiscalledaunitvector
ex calculate andidentifyunitvectors
magnitude
I t.LI r cunitvectors
Incantuan
aFor
what 4,123 aunitvector
scalarkisKxc
14212232 1169 13 K
butalsoitcouldbe becauseitwould
stillbeaunitvector
anyvector ifwedivideitbyitsownmagnitudewegetaunitvectorinthedirectionofit
For
notappearinthetextbook
5specialunitvectors
ifanyvectorit isalreadya
so caned unitvectorthenP I
2 0,17 called
Anyrectorvcanbeexpressed
a10,0 caned as asumofscalarmultiplesof I
aitbitck
Section12.3Dot
P roduct
9 1 1289Iforn wewanttodefinea numerical
quantity that thelenghtsofbothvectorstogetherwithameasurementoft heirrelative
combines
alignment
be ex factor
itrowpointinthesamedirectionalignmentfactor
should
waggement
YfYaymenago In Han
b
, if0istheanglebetweenvowwhentheyaredrawnatthes amestartingpoint
thencos0isthedesiredalignment
Yo i Ew̅ 181181coso
consequences
1 JPIEPsoIPINET
2 ifv18 Fw̅ 0
components Projection
igna
wing
fcomprwl .ro
ftp.fome.fi tiff
jojrw
compit w̅ I
projuw̅ w̅ i i
