given rector dl - math.ucsd.edudstaplet/f20/notes/october 5.pdf · meeee p q 1,44 coil 1 111,3 hp...

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

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

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

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

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

GEOMETRICALLY

A BIT COMPLICATED

RelatingLet E Cain EIR

r Kangfatty

Fuori

So flustfot FEworks in 3D too

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

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

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

THEPOINTI cos corrects

for when I I don't point

in the same direction