Không gian Euclide

7/23/2019 Khng gian Euclide

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t@ h3" tuyn tnh. T: -A tB4 t" sinh, c s v chiDu cEa )h*ng

gian v+cto.

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a. N , P N , P N , Pu v V u v v u =

F. N , ,\ ]P N , P N , P N , Pu v u v w u w v w + = +

c. N , , P N , P N , PR u v V u v u v =

1. N P N , P %^N , P % %u V u u u u u = =

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T#ong )h*ng gian cho ui tc$R

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& $ $ & $ $N , P ^ N , Px x x R y y y R = =

& $ & $ & & & $ $ & $ $N , P NN , P, N , PP $ $ &%x y x x y y x y x y x y x y= = + + +

&. ChVng t N/,yP > tch v* h;ng.$. Tnh tch v* h;ng cEa hai v+ct N$,&P, N&, &Pu v= =

$. Tnh tch v* h;ng cEa hai v+ct >N$,&P, N&, &Pu v= = N , P NN$,&P,N&, &PPu v =

$.& $.$.N &P $.&.& &%.&.N &P &%= + + + =


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$ $& & & $ $ $ $N P ^ N P /d.p x a x b x c q x a x b x c P = + + = + +

T#ong )h*ng gian cho ui tc$[x]P

&

%

N , P N P N Pp q p x q x dx=

&. ChVng t Np,qP > tch v* h;ng.

$. Tnh tch v* h;ng cEa$N P $ ( &, N P &p x x x q x x= + = +

&

%N , P N P. N Pp q p x q x dx=

&$

%N$ ( &PN &Px x x dx= + +

&`

=

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i1 ].

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& $ ( ( & $ ( (N , , P ^ N , , Px x x x R y y y y R = = T#ong )h*ng gian cho ui tc(R

& $ ( & $ (N , P NN , , P,N , , PPx y x x x y y y=

&. ChVng t N/,yP > tch v* h;ng.

$. Tnh tch v* h;ng cEa hai v+ct N$,&,%P, N(, $,LPu v= =

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$. N , P NN$,&,%P,N(, $,LPPu v = .$.( $.$.N $P $.&.( (.&.N $P %.L= + + + +

N , P $$.u v =

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ff ff N , Pu u u= NN(,$,&P,N(,$,&PP=

ff ff .(.( $.(.$ $.$.( (.$.$ &.&u = + + + + ff ff e$u =

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N , P ff ffd u v u v= N , Pu v u v= NN $,$, &P,N $,$, &PP=

N , P .N $P.N $P $.N $P.$ $.$.N $P (.$.$ &.&d u v = + + + +N , P &bd u v =

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N , Pcos

ff ff . ff ff

u v

u v

=&$ &$

`. (& &e`

= =

&$a#ccos

&e`a =

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&. ChVng t Np,qP > tch v* h;ng.

&

&N , P N P N Pp q p x q x dx

=

$. Tnh Np,qP v;i$

N P $ ( & N P (p x x x q x x= + =

&

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=

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=

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=

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ff ff . ff ff

p q

p q=

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&& &

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p(x)q(x)dx

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&. trc giao.M

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M8nh -D

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ChVng 4inh.

HiOn nhiJn.

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+t tch v* h;ng N , Px f & & $ $N , ... Pm mx f f f = + + +

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N , P %x f = hay / vu*ng gAcf.]y / vu*ng gAc v;i .

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T#ong )h*ng gian X( v;i tch v* h;ng chnh tc cho)h*ng gian con

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{& $ (

& $ (& $ (

%N , , P

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x x xF x x x

x x x

+ = = + + =

cho v+ct / m N $, (, 4P. TB4 t6t cG 4 -O / vu*ng gAc v;i .

;c &. TB4 t" sinh cEa NL,R(,&Pw

;c $. vuong goc vi tap sinh cua .x F x F

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ch7 [ tch v* h;ng&.m =

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i1 ]. T" h3"

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[

&. #a$hong gian con cua %.F

$. 1i4N P 1i4N P 1i4F F V+ =

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$

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con cEaR3

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F

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xx

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& (

%$ %

%

x x xx x

x x

+ + = + = =

N , $ , P N&, $,&Px = =




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QiGi. ;c &. TB4 t" sinh cEaF.

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$

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x

x

x

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;c $. Tng t2 nh v 1? t#;c.

]y t" sinh cEaF> N$,R(,&Pw

& $ (

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%$ %x x x

x x x+ + = + =

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ChVng 4inhNFng -" tuyn tnhP

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& & &N , P %u u =

vB S )h*ng chVa v+ct % nJn & &N , P %u u > & % =Tng t2 ta chVng 4inh -3c $ ( ... %m = = = =

]y S -5c >" tuyn tnh.



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ChVng 4inh.

[

QiG s E m e1, e2, ..., enw > c s t#2c chuUn cEa )h*ng

gian _uc>i1 ]. Khi -A v;i 4i , xcA thO Fizu 1izn1uy nh6t 1ng x x1e1! x2e2! ... ! xnenv;i N , P" "x x e=

x V

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v

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v

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^$

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tB4 45t c s t#2c giao, sau -A > c s t#2c chuUn cho 45t)h*ng gian con cEa )h*ng gian _uc>i1.

Cho > h -5c >" tuyn tnh cEa )h*nggian _uc>i1 ].

[ Nu t#Bnh Q#a4 ~ Sch4i1tP

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5.3 8# tr9nh tr:c giao h;a c s t#2c giao cEa .

TB4 $ $ & &f e f= +

$ & $ & & & &N , P N , P N , Pf f e f f f = + $ & & & &% N , P N , Pe f f f = +

$ &&

& &

N , P

N , P

e f

f f

=

( ( ( & & $ $.' dangf f e f f = + +



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5.3 8# tr9nh tr:c giao h;a tt _m N&,%,&,&P, P, N%,&,&,&P,N&,&,&,&Pw

xng u t#Bnh Q#a4 ~Sch4i1t tB4 h t#2c giao, h t#2c chuUn.

LR

& $ ( , , wF f f f= & & N&,%,&,&Pf e= =Chn$ &

$ $ && &

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f e ff f

= TB4

( & ( $( ( & $

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f e f ff f f f

= TB4

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(=

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( ( (

=

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=

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& & & $ ( & & $ $ & &,%, , , , , , , , , ,

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5.3 8# tr9nh tr:c giao h;a 9$ & & $ & `

, , ,% , , , ,` ` ` `` `` `` ``

T#ong )h*ng gian XL v;i tch v* h;ng chnh tc cho

)h*ng gian con

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{ & $ ( L& $ ( L& $ ( L

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+ + = = + + = TB4 chiDu v 45t c s t#2c chuUn cEa .

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TB4 1ng$f$ &

$ $ && &

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N , P

e f

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5.4. H9nh chi # 0#ng g;cA khong cch.------------------------------------------------------------------------------------------

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T#ong )h*ng gian _uc>i1 V cho )h*ng gian con F v

45t v+ct vty [.]+ct v cA thO Fizu 1izn 1uy nh6t 1;i 1ng9

f v f % f F % F = +

v+ct f -3c gi > hBnh chiu vu*ng gAc cEa v/ungF9prFf v=

u coi v+ct v > 45t -iO4, thB -5 1i cEa v+ct % > )hoGng

cch t: v -n )h*ng gian con .

N , P ff ff ff ffd prFv F % v v= =

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&P TB4 hBnh chiu vu*ng gAc cEa v/ungF.

QiGi c0u &P. TB4 45t c s cEaF. QiG s -A >9

v f %= +

$P TB4 )hoGng cch t: v-nF.

& $, ,...,! "mf f f

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& & & $ & $ & & &

& $ & $ $ $ $ $ $

& & $ $

N , P N , P ... N , P N , P N , PN , P N , P ... N , P N , P N , P

... ... ...

N , P N , P ... N , P N , P N , P

m m

m m

m m m m m m m

x f f x f f x f f % f v f



+ + + + = + + + + =

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& $ ( L

& $ ( L

%N , , , P

$ ( ( %

x x x xF x x x x

x x x x

+ + = =

+ + = &P TB4 hBnh chiu vu*ng gAc cEa v+ct /ungF.N&,&,%,&Px=$P TB4 )hoGng cch t: v+ct -nF.N&,&,%,&Px=

&P. TB4 45t c s cEaF9 & $N$, &,&,%P, N $,&,%,&P! "E f f= = = & & & $ & $ &

& $ & $ $ $ $

N , P N , P N , P

N , P N , P N , P

x f f x f f x f

x f f x f f x f

+ = + =

& $

& $

` &

` &

x x

x x

= + =

& $

& &

,&& &&x x

= = & & $ $Fp& x x f x f = +L $ & &

N , , , P&& && && &&

=

$P. N , P ff ff ff ffd prFx F % x x= = b &( & &$

, , ,&& && && &&

= (=

5.4. H9nh chi%# 0#ng g;cA khong cch.


39/40

i s tuyn tnh. Chng !Co"y#ight $%&%Khoa Khoa Hc v K Thut My Tnh (

$P TB4 )hoGng cch t: -nF.

5.4. H9nh chi%# 0#ng g;cA khong cch.------------------------------------------------------------------------------------------

---------------

T#ong )h*ng gian v+ct q$/d v;i tch v* h;ng

&

%N , P N P N Pp q p x q x dx=

Cho )h*ng gian con

] 1?

N P f N&P %! "F p x p= =&P TB4 hBnh chiu cEa /ung F.$N P $ &f x x x= +

$N P $ &f x x x= +

&P. TB4 45t c s cEaF9 $& $, &! "E f x x f x= = =

& & & $ & $ &

& $ & $ $ $ $

N , P N , P N , PN , P N , P N , Pf f f f f ff f f f f f

+ = + =

S 1?ng tch v* h;ng - cho, tB4 h8 "t#Bnh, giGi, tB4 & $,

Suy #a hBnh chiu vu*ng gAc v )hoGng cch.


40/40

Yeu cau.

D =E dng tch 0 h1ng tnh( dFiA khong cchA g;c.

>D T9m c& !G 0F !" chi# c2a I? 0#ng g;c c2a khn gian con.

Thi gian t: hc( t"i thiJ# @ ti%t. )hong KL tng !" gi t: hc.

'D NFm tOt c cc cP# hQi trRc nghi4m 0 khng gian *#c+id S7K cP#.

7D =E dng 6# tr9nh

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