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ER + (A,u)EˆE A+uE @APE,A+⃗0 =A @APE,@u,vPE,A+ (u+v) = (A+u) +v @A,BPE,D!uPE,B=A+u E

E E

E n E n

E E

u tu t ⃗0=E @u,vPE,tu+v=tu˝tv @A,BPE,D!uPE,tu(A) =B

E E

ĕ RE 2 (⃗i,⃗j)EE ??

A B u O j i u

E R E E ɍ + ā

@aPE,a+⃗0 =a @aPE,@u,vPE,a+ (u+v) = (a+u) +v

0 1 2 3 4

0123
AB A B

A= (2,1)

B= (3,3)

ÝÝÑAB= (1,2)

E E n

E

ĕR= (O,B)E B= (e1,e2,...,en)

O ĕ e1,e2,...,en

ĕ ME ÝÝÑOM B

M ĕR x1,x2,...,xnMR

OM=x1e1+x2e2+¨¨¨+xnen

B BB@x 1 x n1 C CCA

ĕRA0

B BB@a 1 a n1 C CCAB0 B BB@b 1 b n1 C

CCA BÝÝÑAB0

B BB@b

1´a1

b n´an1 C CCA (x1,x2,...xn)PK, f(x1,x2,...xn) = 0

R= (O,B)R1= (O1,B1) ĕ E P BB1

B O1R M E X

MR X1 MR1

X=B+PX1

X

1 ÝÝÝÑO1MR1 PX1

ÝÝÝÑO1MR ÝÝÑOM=ÝÝÑOO1+ÝÝÝÑO1M

ÝÝÑOMR X=B+PX1

E E

(A1,A2,...An) n E (λ1,λ2,...λn) n

G ř

(Ai,λi),iPJ1,nK O E ME iÝÝÝÑMAi=ÿ iÝÝÑOAi´ÿ iÝÝÑOM OG=1 iÝÝÑOAi OE

ɍ λi 1

(Ai,λi),iPJ1,nK n E ř

H(Ai,λi),iPJ1,mK

G(Ai,λi),iPJ1,nK (H,ř

J m+ 1,nK

0 =ÿ

iÝÝÑGAi= ÿ i!

ÝÝÑGH+ÿ

iÝÝÑHAi looooooomooooooon ⃗0+ iÝÝÑGAi= ÿ i!

ÝÝÑGH+ÿ

iÝÝÑGAi

E E

F E F EF

F 2

E F

AB A B M

ÝÝÑAM=3

2

ÝÝÑAB M (A,´1

2 )(B,3 2 )(A,´1)(B,3) 2ÝÝÑAM= 3( ÝÝÑAM+ÝÝÑMB) ´ÝÝÑAM+ 3ÝÝÑBM=⃗0 F E

ÝÝÑMNMNF E

F (F)

F (F) 3

E @(A,⃗u)PFˆ(F),A+⃗uPF

F=!ÝÝÑMN,M,NPF)

F ⃗0 =ÝÑAA ɍA F

u,vPF λPR A,B,C,DPF u=ÝÝÑABv=ÝÝÑCD

MPE ÝÝÑAM=u+λv ÝÝÑAM=ÝÝÑAB+λÝÝÑCD=ÝÝÑAB´λÝÑAC+λÝÝÑAD

M (B,1)(C,´λ)(D,λ) MPF u+λvPF

O F=F F

F E A E

F=A+F F E A

F

FA⃗0PF

F E M Mi,iPJ1,nKF

ÝÝÑAM ÝÝÑAMi F ÝÝÑAMPF MPF

FF MN F ÝÝÑMNP(F) ÝÝÑMN=

ÝÝÑAN´ÝÝÑAMPF (F)ĂF uPFB=A+u F

F1 EA F

F1ĂF MPF1 ÝÝÑAMPF MPF

FĂF1 MPF ÝÝÑAMPF ÝÝÑAM=ÝÝÑBC ɍB,CPF1 ÝÝÑAM=ÝÑAC´ÝÝÑAB M (A,1)(B,´1)(C,1) MPF1

F EA F (F) =!ÝÝÑAM,MPF)

ĕ F=(F) F=!

MPE,ÝÝÑAMPF)

uPF M=A+uPFu=ÝÝÑAMPF u=ÝÝÑAMMPF p p

1 2

FG E FG

FĂG FĂG

FĂGFXG FĂG

FG E F=(F)G=(G)

FĂG F=!ÝÝÑMN,M,NPF)

Ă!ÝÝÑMN,M,NPG)

=G

FĂGFXG APFXG

F=!

MPE,ÝÝÑAMPF)

MPE,ÝÝÑAMPG)

=G p

FĂG FĂG (F) =(G) =p F=G

GĂF FXG‰ HF FĂG GĂF

FG E FG FXG

E FXG

FXG‰ H

APFXG F=!

MPE,ÝÝÑAMPF)

G=!

MPE,ÝÝÑAMPG)

FXG=!

MPE,ÝÝÑAMPGÝÝÑAMPF)

MPE,ÝÝÑAMPFXG)

ŗ E A FXG

E

FG E FG

FXG=t0u FXG

FĂG FXG FĂG

0

F+G=E APF,BPG ÝÝÑAB=⃗uloomoon

PF+⃗vloomoon

PG

C=A+⃗u CPF

C=A+⃗u=A+ (ÝÝÑAB+ (´⃗v)) = (A+ÝÝÑAB) + (´⃗v) =B+ (´⃗v)

CPG APF BPG C ⃗u ⃗v

FG E

FXG 2 3 2

ĕ R= (O,⃗i,⃗j)

D E APE F

MPDðñÝÝÑAMPF

F=(⃗u) ɍ⃗uPEzt0u

MPDðñ DtPR,ÝÝÑAM=t⃗u

D=tA+t⃗u,tPRu

A0 a b1 A ⃗u0 β1 A M0 x y1 A

PDðñ DtPR,$

%x=a+tα y=b+tβ

D AA1

⃗u=ÝÝÑAA1 M 0 x y1 A

PDðñ DtPR,M=(A,t),(A1,1´t)

ðñ DtPR,$

%x=ta+ (1´t)a1 y=tb+ (1´t)b1 A0 a b1 A A10 a1 b 11 A D A F

F 2 (⃗i,⃗j)

αx+βy= 0

MPDðñÝÝÑAMPF

ðñα(x´a) +β(y´b) = 0 ɍM0

x y1 A A0 a b1 A

ðñαx+βy=h ɍh=αa+βb

E αx+βy=h ɍ(α,β)‰(0,0)

D:αx+βy= 0 AɍA0

a b1 A

αa+βb=h

D A0 x0 y 01 A ⃗u0 a b1 A M 0quotesdbs_dbs6.pdfusesText_12

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