given rector dl - math.ucsd.edudstaplet/f20/notes/october 5.pdf · meeee p q 1,44 coil 1 111,3 hp...
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oMmddarygOetodba5a.rclass questions
hattieIIntroduced 2B 3D vectors
Vector addition Scalar maltHow to parametrize a 1 he
given point rector
I.IE dlppammtaieeegafoorLi
f Ctl Pt t E
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ExerciseCIA parametrize the line starting
at 142,31 and pointingin the Cl 1,0 direction
2 Try to parameterize theline connecting 14,5 and2 2
O117 air is
a ioi
gs
L param hey 5 It 1213 slitt z t 31t.lt Ago
OrI g Q
ii I iP
L
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Q P starts at P
points to Q
So L has egn
gt CI 22 t to 14,57 21 2
2 2 t t 12 3 f2t2t 243T
The egh for the linefetmeen.pk
Let P Q E IRB or 1122
be two pointsI yi
L L has parametricOa equation
P
Ip FH Pt E CQ P
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If F Xi Yi Zi
and Q Xz yr Zz then
f Ct xitcxz x.lt yitcyz yiltyzitczz z.it
1.20 INNER PRODUCTLENGTH DISTANCEE
There are many waysto
multiply vectors
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Last time solar multiplication
Input vector output vectorreal
THE INNER PRODUCT OR
DOT PRODUCT hes
input 2 vectors output real
IN COORDINATES
x y 2170 Xa Yz Zz
X xztyiyztz TE2 ae
E o 1,2 47013,3 2
31 6 8 1
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GEOMETRICALLY
A BIT COMPLICATED
RelatingLet E Cain EIR
r Kangfatty
Fuori
So flustfot FEworks in 3D too
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Ex we c
find the distance from
f Cia 47to 10,1 1 Q
Imeeee
P Q 1,44 coil 1 111,3
Hp All f ff 3.31
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SOME PROPERTIES
Let DEIR try.IE R2CorlR3
AI dir w D Fair
commutes w
Scalarmulkplicatu
I olv tw t U ovtu.lv
destrinthe
C i J Foucommutative
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MORE GEOMETRYof the DOT PRODUCT
If I RT
Pointone
product oftowegesizott
Theoreira For any pairof 2D fr 3D vectors
I w i
tow AFRAWAH cos
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THEPOINTI cos corrects
for when I I don't point
in the same direction