09/11/17

Leoture#6_

Announcement : . iclickr Tf • first questions : Friday.

Is . register device

#ont.net#iFnE:m:nnt¥>comptv ,i)=v - projfriu )

U

Finding proj and comp graphically :

More line until

#apewrgeaagliagular

it touches To

a¥;H→ sienna-

projftp.rojtcomp.Q#suppose iiandv are a linear

.

What B pro ;( Ii ) ?

¥ it

BFexpressveotorntrmsofamon.us )

The idea & of a basis is to have asntawndaayd

of writingand computing

with vectors .

pphim

.si#heo*

@Fso*#. YejtorisnEagles.rs?#enrT= a

,f + azf Components are

=p ,a + pzpo

w 't i. p

hell = vk.tn#=q2tqT"

t.ve/ample_:Tr=ze+2j Ifill = ZMZ

= ZR a +0.11=2 i.

Changinybasisst,

ah

iEEE¥c*sTo change to the { a ,

I } basis we

expresst and f in terms of these

.

e= projce ,a) + projk ,

d) = # an- fzf

g = projg ,a) tprojblo ) =

€ an xat I

Substitute into (D) for i & j :

=D a =3 # an - tat ) +2 # + fad )= Fa an - fefo ~

this is in the new

basis p. = Fmz

Check : 11 Ilk 113ft zy 11 =ftp.#2=tEilulk 11 Faa - FzToH=¥+# =P

.

Recall : Jr = Zf + Zf = zmz an

t.us = (21+21).(31+21)=6+4--10 -

t.u=(2Ra)•(Faan-faI)=|o]#|All vector operations are basis independent

.

CylindricalCoerdinatesnyyeyeEIYnImtYIIpp@syshortestfrisotannq.x.tshtEEp9Fn3einTd9IfIyeaueu.x

FEI .

"

£r= cosoe + sings ✓

• P'

×

e^o= Exner =E ( code + sin Of )

= cos OF xD + sin O knxf= - sin O

d#+co÷at ) could de changing .