Vectores
September 9, 2022 | Author: Anonymous | Category: N/A
Short Description
Download Vectores...
Description
Y`atkr`s`l `s`l`cpcnlk `s`l `cpcnlk 1.> Y`atkr 1.>
448
O`cksprkdc`jns>nc>9 O`cksprkdc`jns >nc>9`lau`ltr`cnjnflhtuo `lau`ltr`cnjnflhtuoyohr`aahñlo`c yohr`aahñlo`cv`atkronok. v`atkronok. (?,,? ) >. >. v 0 (
(4 ?,, ? ) 4. v 0(
0. v 04 0. 0( (4 ?,,4? )
(4 4,, 1 ) 8. 8. v 0(
1. v 0(( 1,,44 )
9. v 0 (4 4 1,44 )
6. v 0 (( 1,,>)
0( (4 >,,4 1 ) >?. v 0 ( (, >, 4 ) >1. v 04
>0. v 0 (4 0,,2) (
2. v 0 (, (>, 1 )
(4 >,, 1 ) >>. v 0(>, 4 1) 1) >=. v 0(
?. v 0((?,,4? )
>4. v 0 ((1,, 4 )
>> >, 4> ?) ?) >9. v 0(>
>6. Q`n u u 0(4,1)y vv0(40,?).@lau`ltr` n n )1u7 d d ) u u>v7 aa ) vv4u7 o o)4 o)4u46v.Dksqu`e``stks v`atkr`s. >2. Q`n uu 0 41h >4e y vv 0? h > 0e.@lau`ltr`5 nn ) uu > v7 dd ) uu 4 v7 aa ) vv 4 u7 o o) o) ` )4u41v7i i)) uu>4v.Dksqu`e``stks .Dksqu`e``stksv`atkr`s v`atkr`s.. v`atkr`s
.@lau`ltr`n n n)) uu >8. Q`n uu 04 h 41ey v 0 4?h >9e.@lau`ltr` i i)? )?v49u.Dksqu`e``stks .Dksqu`e``stksv`atkr`s v`atkr`s.. v`atkr`s 4=. O`ju`str` O`ju`str`qu``c qu``cv`atkr qu``c v`atkr
44u >1 v7
d) uu 4 v7 aa)1 u7 o o) 46v7 ``)2 u 41 v7 >v 7 d
`sul v`atkrulhtnrhk. ( , 4 )`sulv`atkrulhtnrhk. 1 0
? 0
4>. Ju`str`q Ju`str`qu`cks u`cksv`atkr`s u`cks v`atkr`s hhyesklv`atkr`s sklv`atkr`sulhtnrhks ulhtnrhks.. ulhtnrhks 44. O`ju`str` O`ju`str`qu``c qu``cv`atkr qu``c v`atkr > 4 h > > 4 ee`sulv`atkr `sulv`atkrulhtnrhk ulhtnrhk.. ulhtnrhk
( ) ( )
(
O`ju`str`qu` qu`sh qu` sh vv0nh>deU=,`ltkla`s u 41. O`ju`str` u0 ulhtnrhkqu` ulhtnrhk qu`th`l` qu` th`l`cn th`l` cnjhsjn cnjhsjn jhsjnohr`aahñl ohr`aahñlqu` ohr`aahñl qu` vv.
n
4
4
) (
n > > d h> > d
4
4
n > d
) ee`sulv`atkr
O`cksprkdc`jns4?nc48`lau`ltr`ulv`atk O`cksprkdc`j ns4?nc48`lau`ltr`ulv`atkrulhtnrhk rulhtnrhkqu`t`lfncnjhsjnohr`aa qu`t`lfncnjhsjnohr`aahñlqu``c hñlqu``c v`atkronok. 4?. vv04h>1e
40. v0?h49e
42. vv041h42e
49. v0h4e e
46. v041h>?e
48. v0nh>ne7 nU=
n 1=. Qh vv0nh>deo`ju`str`qu` n ahñlo` vv.
4
4
n n >d 0 aksβy d d
4
4
n n >d 0 s` s`l `l β,oklo` β`scnohr`a-
1>. Qh vv04h41e`lau`ltr`s`l βyaks β. 14. Qh vv0?h4e e`lau`ltr`s`l βyaks β.
Plv`atkr vvth`l`ohr`aahñlkpu`stnncno`cv`atkr uushohr`aahñlo` vv0ohr`aahñlo` u u>ύ.O` cksprkdc`jns11nc12`lau`ltr`ulv`atkrulhtnrhk vvqu`t`lfnohr`aahñlkpu`stn ncnohr`aahñl o`cv`atkronok uu. 11. u0h>e e 16. u044h>1e
1?. u04h41e
10. u0?h49e
19. u041h>?e
12. u041h42e
18. Q`n u u04h 41ey vv04h> 4e.@lau`ltr`ulv`atkrulhtnrhkqu`t`lfncnjhsjnohr`aahñl qu`5 n qu`5 n n)u>v7 dd)4u41v7 aa)1u>2v. Q
?=. Q`n Q`n ] ] ] 0(a (a, o o) o)y ^ ^0(a (a >n, o o >d). Ju`str`qu`cnjnflhtuoo` Ju`str`qu`cnjnflhtuoo` ] ] ] ^ `s Q
4
4
n > d
.
?>. O`ju`str` O`ju`str`qu`cn qu`cnohr`aahñlo` qu`cn ohr`aahñlo` ] ^ `l`cprkdc`jn?=`scnjhsjnqu`cnohr`aahñlo`cv`atkr (n, dd). WQuf`r`lahn5 sh T sh T T 0(n (n, dd),o`ju`str`qu`cnr`atnqu`pnsnpkrckspultks ] ] y ] y ^ ^`s pnrnc`cnncnr`atnqu`pnsnpkrckspultks=y T. pnrnc`cnncnr`atnqu`pnsnpkrckspultks=y T. T.Z T.Z
41= AN]Ê_PCK1 1
Y`atkr`s`l
T4y T1
O`cksprkdc`jns?4nc?6`lau`ltr`ulv`atkr O`cksprkdc`jns?4nc?6 `lau`ltr`ulv`atkr vvqu`t`lfn cnjnflhtuoyohr`aahñlonons. ?4. v
017 β0 ύ 9
?1.
v
0?7 β0 ύ
??.
v
027 β0 ύ 1
?0. v
0>7 β0 ύ ?
?9.
v
047 β0 ύ 4
?6.
v
4ύ 1 097 β 0
*?2. O`ju`str`o`jnl`rnncf` O`ju`str`o`jnl`rnncf`drnhan(`so`ahr drnhan(`so`ahr,`strhatnj`lt`o`cnso`lhahkl`so`sujnyjnfdrnhan(`so`ahr ,`strhatnj`lt`o`cnso`lhahkl`so`sujnyjnflhtuoo`v`atkr`s)qu`pnrnaunc`squh`rnoksv`atkr`s lhtuoo`v`atkr`s)qu`pnrnaunc`squh`rnoks v`atkr`s u uy vv,|u>v| #|u| >|v|. ?8. O`ju`str` O`ju`str`qu` qu`sh qu` sh u uy vvsklohi`r`lt`so`cv`atkra`rk,`ltkla`s|u>v| 0|u| >|v|shysñcksh u`suljõcthpck`sancnrpkshthvko` vv.
N P P _ K @ Y N N C P N A N C N A H Ñ L T @ Q ] P @ Q _ N Q N C NN H. o)
HH. o)
HHH. o)
HY. d)
Y. d0a
JNL@EKO@CNANCAPCNOKTN JNL@EKO@CNANCAPCNOKTN
Q`pu`o`trndnenraklv`atkr`s`lcnancaucnokrnB]0=f.]rhj`rks`c`aahklnjks`c jkoko`akkro`lnonsr`atnlfucnr`spnrncnr`pr`s`ltnahñlo`v`atkr`s,aklcndnlo`rn >66o`cshst`jn`lcnpksha >66o`cshst `jn`lcnpkshahñlo``c`aa hñlo``c`aahñl,nckprh hñl,nckprhjhr jhr fuh`lt`v`ltnln
J_B
|s`pr`s`ltncnsh-
@cj`lõo`Y@A_KTaklth`l`cnsshfuh`lt`siulahkl`s5
Xbnyqu`ns`furnrs`qu`cnkpahñl6`stès`c`aahklnon(`stks`v`rîakjkt`xtkdcnlak skdr`iklokl`frk)
W Z Z Q`pu`o`l`sarhdhrv`atkr`sohr`atnj`lt``lcnphcnuthchznlokcns`au`lahn | @L_@T y`sarhdh` y`sarhdh`lokckslõj`rk lokckslõj`rkss`pnrnok ss`pnrnokspkrakjnsk`spnahks spkrakjnsk`spnahks,lnchznl ,lnchznlokaklcnt`acn okaklcnt`acn , pkr`e`jpck`cv`atkr(1,0)
4?= AN]Ê_PCK1 1
Y`atkr`s`l
T4y T1
Y ]rky kywu0[[[[[[[[[[[[[[ Y. ]r n)
u w w
w
d)
w
a)
u ww w
w
o)
u wu u
u
O`cksprkdc`jns>nc>=ancauc``cprkouatk`sancnro`cksoksv`atkr`sy`caks`lko`c O`cksprkdc`jns>nc>=ancauc``cprkouatk`sancnro` cksoksv`atkr`sy`caks`lko`cîlfuck cksoksv`atkr`sy`caks`lko`c îlfuck `ltr``ccks. >. >. u : h + ee7 v : : h ∔ ee
4. u : : 1h7 v : :∔ : ∔ 6 ee
4h 4 1 ee7 v : 4 1 1 ee 1. u : 4 4 4h >
0h7 v : > >2 2 ee ?. ?. u :∔ : ∔ 0
4 ee7 v : 0h > 6 ee 0. u : ξhh7 v : δ ee7 ξ ,δ r` `n n nc cc` ` `ss 9. u : 4 v 4? h 4 4
6. u : 4h + 0 ee7 v : 6. : 0h+ 4 ee
2. u : 4h + 0 ee7 v : 0h ∔ 4 ee
8. u : ∔ 1 h + ? e7 v : ∔ 4 h ∔ 6 e
0e 7 v e v : : 00hh ∔ ? ee >=. u : ? h + 0
O`ju`str`qu`pnrnaunc`squh`rnlõj`r `rnlõj`rksr`nc`s `rnlõj`r ksr`nc`s ξy δ,cksv`atkr`s uu 0ξh> δey vv 0δh >>. O`ju`str`qu`pnrnaunc`squh 4ξesklkrtkfklnc`s. >4. Q`nl Q`nl uu, vvy w wtr`sv`atkr`snrdhtrnrhks.@xpchqu`pkrquè`cprkouatk u u;v;w lk`stîo`lhok.
O`cksprkdc`jns>1nc>8o`t`rjhl` shcksv`atkr`sonokssklkrtkfklnc`s,pnrnc`cksklhlfulk o`cksoks.O`spuès`sdka`anonpnr. o`cksoks.O`spuès`sdka` anonpnr. 0 e7 v : ∔ 9 h ∔ > >= = ee >1. u : 1 h +
>?. u : 4 h + 1 ee7 v : 9 h ∔ ? e ee
1 ee7 v : 4 9 ee >0. u : 4h 4 4 48 h>
: 9 h + ? ee >9. u : 4h + 1 ee 7 v
4h + >6. u : : 4 + 11 ee7 v : ∔ ∔ 9h + ? ee
>2. u06h7 vv0441e
>8. uu 04h4?e7 vv04h>1e
Q`nl uu01h>?ey vv0h>ξe.O`t`rjhl` ξtncqu`5 4=. Q`nl n) ) u u uy vvsklkrtkfklnc`s. a)
d) ) u u uy vvsklpnrnc`cks.
@cîlfuck`ltr` uuy vv `sύ/?.
o)
@cîlfuck`ltr` uuy vv `sύ/1.
Q`nl uu044h>6ey vv0ξh44e.O`t`rjhl` ξtncqu`5 4>. Q`nl n) uy v vsklkrtkfklnc`s. a)
@cîlfuck`ltr` uuy vv `s4ύ/1.
d) u ) u uy vvsklpnrnc`cks.
o)
@cîlfuck`ltr` uuy vv `sύ/1.
44. @l`cpr @l`cprkdc`jn4=o`ju kdc`jn4=o`ju`str`qu`lk`xh kdc`jn4=o`ju `str`qu`lk`xhst`ulvnckro` `str`qu`lk`xh st`ulvnckro` ξpnrn`cqu` u u y vth`l`lohr`aahkl`s kpu`stns. 41. @l`cprkd @l`cprkdc`jn4>o`ju`str`qu`lk`x c`jn4>o`ju`str`qu`lk`xhst`vnckro` c`jn4>o`ju`str`qu`lk`x hst`vnckro` ξpnrn`cqu` uuy vvth`l`lcnjhsjn ohr`aahñl.
@lcksprkdc`jns4?nc 16ancauc`prkyv u. 4?. uu01h7 vv0h>e
40. u040e7 vv0h>e
49. uu04h41e7 vv048h>9e
42. uu04h>1e7 vv0?h>e 1=. uu0h>e7 vv04h 41e
46. u04h>e7 vv0h44e 48. u04h44e7 vv00h>6e 1>. u0h>e7 vv04h >1e
14. uu0?h4e7 vv044h>1e 11. uu0ξh>δe7 vv0h>e7ξ y δr`nc`s r`nc`spkshthvks pkshthvks
1.4 1.4 @cprkouatk`sancnrycnsprky`aahkl`s`l T4
4?>
1?. uu0h>e7v0ξh>δe7 ξ y δr`nc`spkshthvks 10. uu06h>4e7 vv0?h49e 19. uu0ξh4δe7 vv0h>e7ξ y δr`nc`spkshthvksakl ξ .δ 16. uu0ξh4δe7 vv0h>e7ξ y δr`nc`spkshthvksakl ξ ,δ 12. Q` Q`nl nl uu 0n>h>d>ey vv0n4h>d4e. @stndc @stndc`zanuln `zanulnaklohahñlskdr` `zanuln aklohahñlskdr` nn>, dd>, nn4y dd4qu`ns`fur`
qu` vvyprkyv ut`lfnlcnjhsjn t`lfnlcnjhsjnohr`aahñl. ohr`aahñl. 18. @l`cprkd @l`cprkdc`jn12`stnd c`jn12`stndc`zanulnaklohahñlqu`ns`fur`qu` c`jn12`stnd c`zanulnaklohahñlqu`ns`fur`qu` vyprky v ut`lfnlohr`aahkl`s kpu`stns. Q
Q
?=. Q` Q`nl nl ] ] 0(4,1), ^ ^ 0(0,6), T T 0(4, 41)y Q Q0(>,4).Ancauc`prky ] ^ TQyprky TQ] ^ . Q
Q
Q
Q
?>. Q`nl ] ] 0(4>,1), ^ ^ 0(4,?), T T 0(49, 44)y Q Q0(1,=).Ancauc`prky] ^ TQyprkyTQ] ^. Q
Q
]ru`d`qu`cksv`atkr`s cksv`atkr`sohi`r`lt`so`a`r cksv`atkr`s ohi`r`lt`so`a`rk ohi`r`lt`so`a`r k u ?4. ]ru`d`qu` uy vsklpnrnc`cksshysñcksh vv 0ξupnrnncfuln aklstnlt` ξ.WQuf`r`lahn5 O`ju`str`qu`aks ϐ0¾>shysñcksh vv0ξu.Z ]ru`d`qu` qu` uuy vvsklkrtkfklnc`sshysñck sklkrtkfklnc`sshysñcksh sh uu ; v0=. ?1. ]ru`d` ??. O`ju`str` O`ju`str`qu``c qu``cv`atkr qu``c v`atkr vv0nh>de`skrtkfklncncnr`atn nx nx >dy >a 0=. ?0. O`ju`str` O`ju`str`qu``c qu``cv`atkr qu``c v`atkr uu0dh>ne`spnrnc`ckncnr`atn nx nx >dy >a 0=.
Pltrhîlfuckth`l`vèrtha`s(>, th`l`vèrtha`s(>,1),(?, th`l`vèrtha`s(>, 1),(?, 44)y(41,9).@lau`ltr``caks`lko` 1,9).@lau`ltr``caks`lko`anonîlfuck. anonîlfuck. ?9. Pltrhîlfuck Pltrhîlfuckth`l`vèrtha`s th`l`vèrtha`s((n>, d th`l`vèrtha`s d>),(n4, d d4)y(n1, d d1). @lau`ltr`cniñrjucnpnrn`caks`lko` ?6. Pltrhîlfuck anonîlfuck. *?2. Cn o`shfunconoo`Anuaby-Qabwnrz`stndc`a`qu`pnrn `stndc`a`qu`pnrnaunc`squh`rnlõj`rksr`nc`s aunc`squh`rnlõj`rksr`nc`sn>, n n4,d> y dd4 /4 >/
>//4 44
4 4 4 4 n d ≯ ∞ ∞::> ∞ ∞::> n ∞:> d 4
g g
g
g g
g
g
g
g
Pthcha``cprkouatk`sancnrpnrnprkdnr`stniñrjucn.»Dnekquèahraulstnlahnss`pu`o`susthtuhrcno`shfunconopkrulnhfuncono; ]ru`d`qu`cnohstnlahnjîsakrtn`ltr`ulpultkyulnr`atns`jho`pk rtn`ltr`ulpultkyulnr`atns`jho`pkrulncêl`nqu` rtn`ltr`ulpultkyulnr`atns`jho`pk rulncêl`nqu` *?8. ]ru`d`qu`cnohstnlahnjîsak pnsnpkr`cpultky`sp`rp`lohaucnrncnr`atn. 0=. @lau`ltr`c @lau`ltr`cnohstnlahn nohstnlahn`ltr` nohstnlahn `ltr` ] ] 0(4,1)ycnr`atnqu`pnsnpkrckspultks ^ T 0 (1,0).
0( 4>,6)y
0>. @lau`ltr`cnohstnlahn`ltr`(1,6)ycnr `ltr`(1,6)ycnr`atnqu`vnnck `ltr`(1,6)ycnr`atnqu`vnnck `atnqu`vnnckcnrfko`cv cnrfko`cv`atkr cnrfko`cv `atkr vv04h41equ`pnsn pkr`ckrhf`l.
4tncqu`anonakcujln`sulv`atkr ln`sulv`atkrulhtnrhk ulhtnrhkyqu`cnsoksakyqu`cnsoksak04. Q`n N Nulnjntrhzo`4 14tncqu`anonakcuj > t cujlnssklkrtkfklnc`s cujlnsskl krtkfklnc`s.O`ju`str` krtkfklnc`s .O`ju`str`qu` .O`ju`str` qu` N N `shlv`rthdc`yqu` N N 0N (N s`aklka`akjk jntrhz krtkfklnc krtkfklnc). 4
T @ Q ] P @ Q _ N Q N C NN N P P _ K @ Y N C N N C P N A N A H Ñ L H.
a)
HH. d)
HHH.
d)
HY. HY. a)
Y. a)
@cprkouatkaruzo`oksv`atkr`s `atkr`s 1.? @cprkouatkaruzo`oksv 1.?
49>
@lcksprkdc`jns @lcksprkdc`jns>nc49 >nc49`lau`ltr``cprkouatk `lau`ltr``cprkouatkaruz aruz u1v. >. u0h44e7 v01g
4. u01h46e7v0h>g
1. u04h41e7 v048h>9e
?. u0h4e7 e7 v0e>g
0. u046g7 v0e>4g
9. u04h46g7v041h4?e
6. u044h>1e7 v0 6h>?g
2. u0nh>de7 v0 ah>o e
8. u0nh>dg7 v0 ah>og
>=. u0ne>dg7 v0 ah>og
>>. >>. u04h41e>g7 v0 h>4e>g
>4. u01h4?e>4g7 v0 9h41e>0g
>1. u0h>4e>g7 v04h>9e4g
>?. u041h44e>g7 v0 9h>?e44g
>0. >0. u0h>6e41g7 v04h46e>1g
>9. u0h46e41g7 v04h>6e41g
>6. >6. u04h41e>0g7 v0 1h4e e4g
>2. u0nh>de>ag7 v0 h>e e>g
>8. >8. u0>=h>6e41g7 v041h>?e41g
4=. u04h>?e49g7 v04h4e e>1g
4>. 4>. u04h44e>0g7 v044h>?e>2g
e>g7 v0 ?h>4e>4g 44. u04h4e
41. 41. u01h4e e>2g7 v0 h>e e4?g
4?. u0nh>ne>ng7 v0 dh>de>dg
40. 40. u0nh>de>ag7 v0 nh>de4ag
49. u04?h41e>0g7 v04h41e41g
46. @lau`ltr`oksv`atkr`sulhtnrhkskrtkfklnc`stnltkn u04h41eakjkn v0?e>1g. 42. @lau`ltr`oks @lau`ltr`oksv`atkr`sulhtnrhks v`atkr`sulhtnrhkskrtkfklnc`stnltk krtkfklnc`stnltkn n u0h>e e>gakjkn v0h 4e 4g. 48. Pthcha``cprkouatkaruzpnrn`lakltrnr`cs`lko`cîlfuck ϐ ϐ`ltr`cksv`atkr`s u04 h >ee 4gy v041h44e>?g. 1=. Pthcha``cprkouatk`sancnrpnrnancaucnr`caks`lk Pthcha``cprkouatk`sancnrpnrnancaucnr`caks`lko`cîlfuck o`cîlfuck ϐ `ltr`cksv`atkr`so`cprkprkϐ`ltr`cksv`atkr`so`c 4 4 dc`jn48.O`spuèso`ju`str`qu`pnrncksvnckr`sancaucnoks,s`l dc`jn48.O`spuèso`ju`str`qu` pnrncksvnckr`sancaucnoks,s`l ϐ>aks ϐ0>.
@lcksprkdc`jns1>nc19`lau`ltr``cîr`no`cpnrnc`ckfrnjkaklcksvèrtha`snoyna`lt`sonoks. 1>. (>, 44,1)7(4,=,>)7(=,?,=)
14. (44,>,>)7(4,4,1)7(4>, 44,?)
11. (44,>,=)7(>,?,4)7(41,>,0)
1?. (6, 44, 41)7(4?,>,9)7(0, 44,1)
10. (n,=,=)7(=, ,=,=)7(=, d dd,=)7(=,=, ,=)7(=,=, a aa)
19. (n, d d,=)7( ,=)7(n n,=, ,=, d d d)7(=, )7(=, n nn, d d)
O`ju`str`qu`| qu`|u1v |40| u|4|v|44( u ; v)4.W .WQuf`r`lahn5 Quf`r`lahn5 @sarêdnck`ltèrjhlkso`akjpk16. O`ju`str` l`lt`s.Z 12. Pthcha`cnsprkph`ono`s>,?,4y1 Pthcha`cnsprkph`ono`s>,?,4y1(`l`s`kro`l)`l (`l`s`kro`l)`lcns`aahñl4.4pnrnprkdnrcnspnrt`s (`l`s`kro`l)`l cns`aahñl4.4pnrnprkdnrcnspnrt`s h cns`aahñl4.4pnrnprkdnrcnspnrt`s h h), ), hh), hhh )),, hhh hhh)y )y hv )y hv hv hv))o`ct`kr`jn4. 18. ]ru`d``ct`kr`jn4pnrt` ]ru`d``ct`kr`jn4pnrt` v vv)`sarhdh`lokcnsakjpkl`lt`so`anon )`sarhdh`lokcnsakjpkl`lt`so`anoncnoko`cnhfuncono. cnoko`cnhfuncono. ?=. ]ru`d``ct`kr`jn4pnrt` ]ru`d``ct`kr`jn4pnrt` vh). WQuf`r`lahn5 Pthcha`cnspnrt`s hh) ) y vv)y`cb`abko`qu``c )y prkouatk`sancnr`sakljutnthvkpnrno`jkstrnr prkouatk`sancnr`sakljutnthvk pnrno`jkstrnrqu` qu` u ; (u 1v) 04u ; (u1v).Z ?>. ]ru`d``ct`kr`jn4pnrt` ]ru`d``ct`kr`jn4pnrt` vhh vhh vhh). WQuf`r`lahn5 Ps``ct`kr`jn Ps``ct`kr`jn1.1.1,pîf.40=, 1.1.1,pîf.40=,cnprkph`ono9, cnprkph`ono9, pîf.>8=ycn`aunahñl(4).Z
(n>, dd>, aa>), v0(n (n4, dd4,a4)y w0(n (n1, d ?4. O`ju`str`qu`sh u0(n d1, aa1),`ltkla`s
u u
⋀⋀( ÖÖ v v
w
):
n n>>
> d d>
a>
n n44
d d4 4
a4
n n11
d d1 1
a1
494 AN]Ê_PCK1 1
T4y T1
Y`atkr`s`l
?1. Ancauc``cvkcuj`lo`cpnrnc`c`pêp`oko`t`rjhlnokpkrcksv`atkr`s h4e e,1h>4g, 46e>1g. Q
Q
Q
]^, ] ]T y ] ]Q,oklo` Ancauc``cvkcuj`lo`cpnrnc`c`pêp`oko`t`rjhlnokpkrcksv`atkr`s pkrcksv`atkr`s ] ??. Ancauc``cvkcuj`lo`cpnrnc`c`pêp`oko`t`rjhlnok ] 0(4,>, 4>), ^ >), ^ ^ 0(41,>,?), 1,>,?), T T T 0(4>,=,4)y >,=,4)y Q Q Q 0(41, 4>,0). ?0. @c vkcuj`lf`l`rnokpkrtr`sv`atkr`s u, v y w `l 1`stîo`lhokakjk`cvkcuj`lo`c pnrnc`c`pêp`okauykscnoksskl u, vy w(akjk`lcnfurn1.14).Q`n N N ulnjntrhzo`1 11 ys`nl u>0Nu, v>0Nvy w>0Nwo`ju`str`qu`
**
Ykcuj`lf`l`rnokpkru>, v>, w>0(9o`t o`t N N N)(vkcuj`lf`l`rnokpkru, v, w).
@stkju`strn @stkju`strnqu``c qu``co`t`rjhlnlt`o` o`t`rjhlnlt`o`uln uln ulnjntrhzo`4 jntrhzo`4 14jucthpchan`cîr`n,`co`t`rjh lnlt`o` ulnjntrhzo`1 11jucthpchan`cvkcuj`l. 1jucthpchan`cvkcuj`l.
?9.
4 Q`n N 0 ? >
1 >
0 , 9
4>
=
u
4 0 4> , =
v
> 0 = ?
y
w
4> 1. 0 4
n)
Ancauc``cvkcuj`l Ancauc``c vkcuj`lf`l`rnokpkr vkcuj`l f`l`rnokpkr u, vy w.
d)
Ancauc``cvkcuj`l Ancauc``c vkcuj`lf`l`rnokpkr vkcuj`l f`l`rnokpkr Nu, N Nvy N Nw.
a)
Ancauc`o`t Ancauc` o`t N o`t N N.
o)
O`ju`str`qu`Wvkcuj`l O`ju`str`qu `Wvkcuj`l`l`chlahsk `Wvkcuj`l `l`chlahsk d)Z )Z0(9o`t o`t N N N)1Wvkcuj`l`l`chlahsk Wvkcuj`l`l`chlahsk n nn)Z )Z..
?6. @c trhpc`prkouatkaruzo`tr`sv`atkr`s`l 1 `stîo`lhokakjk`cv`atkr u1(v1w).O`ju`str`qu` u1(v1w) 0(u;w)v4(u ;v)w N P P _ K @ Y N N C P N A N C N A H Ñ L T @ Q ] P @ Q _ N Q N C NN
H. H. o o)
HH. a a)
HHH. d d)0v`atkra`rkWLktn5h 1e 1g `stî `stîo`lhok
pkrqu` (h 1e) 1g 0= 0h 1We 1g)Z HY. o HY. o)
Y. n n)
YH. a a)0v`atkra`rk
JNL@EKO@CNANCAPCNOKTN JNL@EKO@CNANCAPCNOKTN
@cprkouatkaruzo`oksv`atkr`ss` pu`o``lakltrnrohr`atnj`lt`uthchznlok`cakjnlokATKQQ,`stk`s W Z Z
1
W Z Z
0 NC]BN
NC]BN NC]BN
A
Q]A
T
0 @L_@T
9
1 @L_@T
K
Q
Q @L_@T
@lcksprkdc`jns?2nc0>ancauc` u1vaklancaucnokrn. ?2. u0(4=.1?9, 4=.0>6, 4=.24?)7 v0(4=.0>6,=.2>>,=.641) ?8. u0(4>0,46,21)7 v0(42?, 466,0>) 0=. u0(=.=4?,=.=19,=.=00)7 v0(=.=22, 4=.=9?,=.=16) 0>. u0(04?>, 41>88,4129)7 v0(>6?4,2411,8?>9)
View more...
Comments