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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oMmddarygO etodba5a.r class questions hattie IIntroduced 2B 3D vectors Vector addition Scalar malt How to parametrize a 1 he given point rector I.IE dl ppammtaieeegafoorLi f Ctl Pt t E

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Page 1: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 2: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 3: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 4: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 5: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 6: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

GEOMETRICALLY

A BIT COMPLICATED

RelatingLet E Cain EIR

r Kangfatty

Fuori

So flustfot FEworks in 3D too

Page 7: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 8: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 9: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

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

Page 10: given rector dl - math.ucsd.edudstaplet/F20/Notes/October 5.pdf · meeee P Q 1,44 coil 1 111,3 Hp All f ff 3.31. SOME PROPERTIES Let DEIR try.IE R2CorlR3 AI dir w D Fair commutes

THEPOINTI cos corrects

for when I I don't point

in the same direction