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šFus5“Á†’‚xWÉGus5ˆ‰uzƒŒ{~ŒUusˀKvusvŽUuwÚ^íKw|w|uw˗|u

Ã

Ž9gÅ?ˆµ}KvŽUu»“’x^w˜}Kuwá†Ä‡s{ºu»w|uz|“:uwËżÞ

rtsvuaˆµu»ÄßXëG}^Ž9zƒuaˆµu–sˆŽ„‡†ˆµ€Fx^wƒ€Kˆµë?†|wƒÚFŽœ†w|‚7Û

Ã

}ŒU~ã^†|€XÞ*uaswƒáasv€uˆ<–ŒUs¼ŽUuŒ9s†|“½{ºŠƒŒ‚|sutÊ)usvà

ŽUuŒ‰uw

1

ÉGuŒUu€K†|w|€^uawËÅ^֏zƒŒ*„=†ˆ‰ˆUxW€u€uazx^¼Ž*ˆ‰}KvŽ‰u‚x^z|uŒ*x^†|{?uZŽRÊxt{~}K€uw|‚ƒuaw”šƒxTŽUáÚ}w|ÚFŒ‰uà

Ž9sˆUsvuŒ‰ŽœÊ)uŒU‚ƒuw=9'Rr‡uŒ<*uÚFŽU}^Œa—‚ƒuŒ=‚ƒuawÚXusw|ˆŽUuw„=ɍˆŽMx^w|‚áZÊ=sˆ‰yMzƒuwáÊ)usjÊ=sw|‚ˆ‰y9zsvu{ºuw

ȇuŒMxW‚|uws“½˜‡xW†“ ÉGuˆUy9zƒŒ‰uasvɃŽa—ˆµŽ‰uazŽ=ˆµuawƒÚFŒUuy9zKŽ‡x^†|{ ÉGus‚|uw1ȇuŒ9x^‚|uwËÅ)

(3)

“’xTŽ9sˆ‰y9z”~ã^Ž)ˆUsyMz”‚|suˆµuŒšƒx^y9z

Ã

uŒ9zx^¼Žˆ‰uzƒŒ)usy9zKŽ“:svŽ)ćs{~ut‚ƒuˆš|xTŽ‰áuˆ

Ã

}Kw”Æ-ßFŽ9zxW€}Œ9x^ˆ

ÉGuu€uw˗|Ê=svu#„ɍɍs‚|†|w|€ç–áusv€^ŽaÅ

HH HH

HH HH

H H H H H H H H

h

g

@ @

@ q q

/

-?

„=É|É?s‚|†|wƒ€ç@9r‡uŒ„=ɍˆµŽ9x^w‚|ˆ

Ã

uÚFŽ‰}ŒÊ=sw|‚|ˆUy9z|su{~uŒtȇuŒ9x^‚ƒuw

r‡uŒA*uŒ‰Ésw|‚|†|w|€Kˆ

Ã

uÚKŽU}Œ

−→

/ ˆµus=‚ƒuŒC„É?ˆŽMx^w|‚|ˆ

Ã

uÚKŽU}Œ”‚ƒuŒ¥ÈtuŒ9x^‚ƒuw

g

†|w|‚

h

Å)æ^u‚|uŒ

Æ*†|wƒÚFŽ7?

6

=

∈ h

ɍs‚|uZŽÁ“:svŽ‚ƒuaw Æ*†|wƒÚFŽ‰uawB/†w|‚C™‚ƒu“’wx^y9z7usw7Œ‰uay9zŽRÊ=swƒÚƒs€uˆ

r‡Œ‰usuyUÚjŃÜtx^y9z¥‚|u“½š|xaŽUᖂƒuˆÆ-ßFŽ9z?xT€}Œ9x^ˆ)€s¼Ž‚x^w|w

| −−→

/-?

| 2 = | −→

/

| 2 + | −−→

-?

| 2

—FÊ)}Œ9x^†|ˆ

{~}K€^Ž!9

| −−→

/-?

| ≥ | −→

/

|

„‡wx^v}€u1ì|}K€uŒU†|wƒ€uawä€ua¼ŽUuwè{ºŠƒŒ¥x^u1ƆwƒÚKŽUuD/E?

6

=

/

∈ g

Å*r–x^“:svŽ”ɍs‚ƒuŽ

−→

/ ‚ƒuw

ÚXusw|ˆŽUuw„=É?ˆŽMx^w|‚ËÅ

î…x^wÚ^x^w|w1‚|suˆÊ=su‚ƒuŒ9†|“xW“0ìGx^‚ƒuw|“:}X‚|u ÉGuvu€uw˗Êuw|w1“’x^wáÅþ‡Åj‚x^ˆ‡â"x^{ºu¼àÈtu}^à

‚ƒŒ‰uasvuy9Ú:†|w‚’uswƒuw”ìGx^‚ƒuw’ᆔćs{ºu‡w|s“’“»ŽaÅFî…x^w”zã^¼ŽwF†w”‚x^ˆÈ‡u}ƒ‚ƒŒ‰usuy9Ú:s“ Æ*†|wƒÚFŽF/

ˆµuawƒÚFŒ‰uay9zKŽ–x^w‚|su+ȇuŒ9x^‚ƒu

g

†|w|‚ɍs‚ƒuŽtˆµ}K“:svŽ‡“’s¼Žt‚ƒuŒG»x^wŽUuÁ‚ƒuw&uŒ‰Ésw‚|†|w|€ˆ

Ã

uÚKŽU}Œ

−→

/ w?x^y9zËÅKî1svŽ ćs{~u=‚ƒuˆ*ì?x^‚|uw|ˆÚWx^ww:“’x^w:wX†|w:áus€uw˗K‚x<:Rua‚ƒu‚|uwƒÚXÉ?xWŒ‰u‡šFŽUŒ‰uyUÚu=x^†{

‚ƒuwÉjus‚|uw}ÉGuw1‚xWŒ‰€uˆµŽUuvŽUuw1r‡Œ‰usuyUÚuw…ã^wƒ€uŒtsˆŽ–x^ˆ‡‚|svu

Ã

}K“ȇu}ƒ‚ƒŒ‰usuy9ÚÉGuu€^ŽUu

*uÚKŽU}ŒU~ã^wƒ€uÅ

H 6 ü÷ËÓ òÐ¥ö÷5ü…Òœõ"ÒøùÐ:ÔÐCÕ

sŒÊ=sˆ‰ˆµuawåwX†|w˗‚x…uswIuÚKŽU}Œ—"‚|uŒ+‚ƒuawïڃvusw|ˆŽUuawê„É?ˆŽMx^w|‚ïáÊ=sˆ‰yMzƒuwåáZÊ)us*Ê=sw|‚ƒà

ˆ‰yMz|su{~uw1ȇuŒ9x^‚|uw¥ÉGuˆ‰yMzƒŒ‰usÉƒŽa—|ˆ‰uwƒÚXŒ‰uy9zKŽ‡xW†{ÉGus‚ƒuw1ȇuŒ9x^‚ƒuawˆŽUuzŽaÅ|rtsuˆµu#þ u‚swƒ€K†wƒ€

Ú^x^w|w“’x^w{ºŠ|Œ‚|su»þ)uŒ‰uay9z|wX†|wƒ€”‚ƒuˆ„=ɍˆŽMx^w|‚|uˆœzƒuŒ9x^wƒásuzƒuw5Å

þ)uZŽUŒ9x^y9zŽUuawCÊ=svŒ=‚|sutÊ=sw|‚|ˆUy9z|su{~uaw1ȇuŒ9x^‚|uw

g : X ~ =

 − 3 9 0

| {z }

G

 4

− 1 8

| {z }

~ u

†|w‚

h : X ~ =

 8 4 4

| {z }

H

 4 3 4

| {z }

~ v

‚ƒuŒUuwτ=ɍˆµŽMx^w|‚Ïs“ ì}Kv€uw|‚|uwÏÉGuˆŽ9s“:“#ŽCÊ)uŒ9‚ƒuw ˆµ}K¹Å„‡†|{#‚ƒuw ÜtxWyMzÊ)uasˆ—)‚?xä‚|svu

ȇuŒMxW‚|uw’Ê=sw|‚|ˆUy9zsvu{ˆUsw|‚5—FÊ=svŒU‚¥z|suŒ

Ã

uŒ‰áasy9zKŽUuZŽaŃrtsvu7J#r‡uŒ€uwƒus€^ŽUutÂ5uaˆµuŒ‰Öw¥“+í€utsz|w

ˆµuavɍˆµŽuŒ‰É|Œ9swƒ€uw5Å

KFLNM OQP=R+ST<UPV>W0X*XZYP\[]P^*_Pa`cbCd_efR

sŒÉGuˆŽ9s“:“+uawF:Ruuswƒuw»Æ*†|w|ÚKŽxW†{X‚ƒuŒÈ‡uŒ9x^‚|uw

g

É|áÊ#Åax^†|{X‚ƒuŒÈ‡uŒMxW‚|uw

h

ÅTȇŒ9†|w|‚|s‚ƒuu

‚|suˆµuŒ#îuZŽ9zƒ}ƒ‚ƒu’sˆµŽa—5‚x“”x^w ‚|suˆµu’ÉGus‚|uw7Æ*†|w|ÚKŽUu”x^†|{ ‚ƒuawg:RuZÊ)uss€uwåȇuŒ9x^‚ƒuaw7{~Œ‰us

(4)

Ã

“Á†»“”x^w+‚svu=Æ*†|wƒÚFŽ‰u=ˆµ}

Ã

uŒUˆ‰yMz|suÉGuw:Ú^íKw|w|uw˗K‚?x»‚|suˆ‰uŒh*uÚKŽU}Œ*ˆµuw|ÚFŒ‰uay9zŽxW†{?ÉGus‚ƒuw

ȇuŒMxW‚|uw7ˆŽUuzŽ†|w|‚7ˆ‰}“’s¼Ž#‚ƒuaw „=É?ˆŽMx^w|‚|ˆ

Ã

uÚFŽU}Œ–Œ‰u덌9ã^ˆµuwKŽ9svuŒµŽaÅ5î…x^w ɍs‚ƒuŽ7,X†x^ˆ‰s‚x^ˆ

}ÉGuwÉGuˆ‰yMzƒŒUsuÉGuwƒu#þ)uˆ‰uw|ˆµŽUsuvàÇî}ƒ‚ƒu5wx^yMzËÅ

rtsvu#Æ*†|wƒÚFŽUu#x^†{ ‚|uŒ‡È‡uŒ9x^‚ƒuw

g

Ê)uŒU‚ƒuaw¥Éjuˆ‰yMzƒŒUsvuÉGuw‚|†ƒŒUyMz‚|uwi ‡ŒµŽ9ˆ

Ã

uÚKŽU}Œ

X ~ g =

 − 3 + 4λ 9 − λ

„‡wx^v}€’{º}Kv€^Ž={ºŠ|ŒœuswƒuwÉGusvuÉ?sv€uwƆwƒÚKŽtxW†{ ‚|uŒ‡È‡uŒ9x^‚ƒuw

h X ~ h =

 8 + 4µ 4 + 3µ 4 + 4µ

r‡uŒ*uŒ‰É?sw|‚†|wƒ€Kˆ

Ã

uÚFŽU}ŒœáZÊ=sˆ‰yMzƒuw‚ƒuwÉGus‚ƒuwÆ*†|wƒÚFŽUuwzxTŽ=‚ƒu“’wx^y9z‚|svu#ì}ŒU“

−−−→ X g X h =

 11 + 4µ − 4λ

− 5 + 3µ + λ 4 + 4µ − 8λ

܇†|wCˆµ}K

−−−→ X g X h

ˆ‰uwƒÚXŒ‰uy9zKŽœx^†|{ËÉGus‚ƒuwȇuŒ9x^‚ƒuwCˆŽUuzƒuaw˗X‚ËÅzËÅ

λ

†|w‚

µ

“Š|ˆUˆµuw”‚|u“+uawŽ‰à

ˆµëŒ‰uy9z|uw|‚€uZʜã^z|vŽœÊ)uŒU‚|uwËÅ

rtsvušXy9zXŠ|vuŒ‰Öw|wƒuw刵}KvŽUuwåx^w ‚svuˆ‰uŒ:šKŽUuvuCˆµuavɍˆµŽMã^w|‚|s€1‚|suC“+uZŽ9zƒ}ƒ‚|sˆ‰yMzƒuj*uŒ‰É?sw|‚†|wƒ€

á†|“šFÚ^x^xWŒ‰ëŒ‰}X‚†ƒÚKŽtzƒuŒUˆµŽUuuwïÛ¹Â5uŒUwƒuawx^ˆœ€u‚?x^wƒÚXsyMzƒuk*uŒUwƒuŽ‰áa†|wƒ€XÞMÅGšƒsvuˆµ}K¼ŽUuw{~uŒµà

wƒuŒ¥Ê=sˆ‰ˆ‰uwlJ

Ã

uŒUˆµŽ9x^w‚ƒuwÏz?xTÉGuaw˗‚x䓒x^wς|su ˜sy9zKŽ9†|wƒ€Kˆ

Ã

uÚFŽ‰}Œ‰uaw4uswƒuŒ1ȇuŒ9x^‚ƒu7{~Œ‰us

uwKŽU~x^wƒ€7‚|svuaˆµuŒ

Ã

uŒUˆ‰yMz|suÉGuwåÚ^x^w|w Û¹ˆ‰suzƒu„=ɍˆUy9z|ws¼Ž‰ŽmXŐçTÞMÅ"rtsušXyMz|†ˆ‰ˆ‰{º}Kv€uŒU†wƒ€—‚?x|—

‚x傃uŒnuÚFŽU}Œ

−−−→ X g X h

x^†|{»ÉGus‚ƒuw ˜sy9zKŽU†wƒ€Kˆ

Ã

uÚKŽU}Œ‰uawψµuawƒÚFŒ‰uay9zŽˆŽUuzƒuw ˆµ}K¹—‚ƒuŒ‰uaw

šFÚ^x^xWŒ‰ëŒ‰}ƒ‚|†ƒÚFŽ€Kvusy9z܇†|5ˆµusw“Á†—|Ú^}K“’“»Ž=‚x^w|w¥ŒUuy9zKŽ=ˆ‰yMz|wƒuËᆍˆŽMx^w|‚ƒuKÅ

„‡†|ˆœ‚svuˆ‰uw

1

ÉGuŒUu€K†|wƒ€uaw¥uŒ‰€KsÉƒŽ=ˆ‰sy9zuswsw|uaxWŒ‰uˆ‡ÈtusyMzF†wƒ€Kˆ‰ˆµßƒˆŽUu“

−−−→ X g X h T

· ~u = 0 : 4(11 + 4µ − 4λ) − ( − 5 + 3µ + λ) + 8(4 + 4µ − 8λ) = 0

−−−→ X g X h T

· ~v = 0 : 4(11 + 4µ − 4λ) + 3( − 5 + 3µ + λ) + 4(4 + 4µ − 8λ) = 0 81 + 45µ − 81λ = 0 45 + 41µ − 45λ = 0

“:svŽ=‚ƒuwÂ5íKˆ‰†wƒ€uw

λ = 1

†|w‚

µ = 0

Å

λ = 1

uswƒ€uˆµuŽ‰áŽsw

g

uŒ‰€KsÉƒŽE/ÁÛµçpoqroqKÞM—

µ = 0

sw

h

uswƒ€uˆ‰uZŽUáZŽ#uŒU€sÉƒŽk:ÛsqloÀtoÀXÞMŕswƒu x^€u“+uaswƒu–r–xWŒUˆŽUu†wƒ€+‚|uˆ„=ɍˆŽMx^w|‚|ˆ

Ã

uÚKŽU}ŒUˆ €uZÊ=sw|wKŽœ“’x^w¥wF†|w5—FÊ)uw|w¥“”xWw¥‚ƒuw*uŒµà

ɍsw|‚|†wƒ€Kˆ

Ã

uÚKŽU}Œ

−−→ U V

ɍs‚ƒuŽ+†|w‚êx^ˆÁ˜sy9zKŽ9†|wƒ€Kˆ

Ã

uÚFŽU}^Œ:x^†ƒÿËx^Ž

x^ˆ:šKŽ9ŠƒŽ‰á

Ã

uÚFŽU}ŒÚ^x^w|w

‚ƒuŒG =ŒµŽ9ˆ

Ã

uÚFŽU}Œ

Ã

}Kw

U

Ûg}X‚|uŒ

V

Þ)‚|suwƒuaw=9

~n : X ~ =

 8 4 4

 + ν

 − 7 4 4

r‡uŒ„=É?ˆŽMx^w|‚¥ÉjuŒ‰uy9zwƒuZŽ=ˆUsyMz¥á†

d(g, h) = | −→

/

| = 9

KFLZu OQP=R+ST<UPVvDP\efRpTw`+ehP=R#RP

î…x^wÉGuˆŽ9s“:“#Ž‡x^†|ˆ=‚ƒuŒ=þ)u‚|swƒ€K†|wƒ€—G‚x”‚ƒuŒ‡„=ɍˆŽMx^w|‚ˆ

Ã

uÚKŽU}Œ

−−→ U V

ˆµuw|ÚFŒ‰uyMzŽ–x^†|{"ÉGus¼à

‚ƒuwÈtuŒ9x^‚ƒuwCˆŽUuzKŽ—Fᆍwã^y9zˆŽ‚|uˆ‰ˆ‰uwC˜syMzŽ9†|w|€Kˆ

Ã

uÚKŽU}Œ

→ n

ÅXr–x^w|w”ÉGuZŽUŒ9x^yMzŽUuZŽ“’x^w’uaswƒu

€uˆUy9z|}Kˆ‰ˆµuawƒuG*uÚFŽ‰}Œ‰ÚuZŽ‰ŽUu–€u“’ã’„=É|ɍs‚†|wƒ€¥¾FÅ

(5)

HH HH

HH HH

H H H H H H H H

g

h r

U

V r G r

r H

p 6 p

−−→ V U = σ~n

+

−−→ U G = λ~u

+ ~u

−−→ GH H H H Y ~v

HHH

HH HH j

−−→ HV = µ~v

„=É|ɍs‚|†wƒ€C¾p9Gȇuaˆ‰y9zv}Kˆ‰ˆ‰uwƒu>uÚKŽU}Œ‰Ú^uŽµŽUu

r‡uŒ˜=syMzŽ9†|w|€ˆ

Ã

uÚKŽU}Œ

~n

ˆµŽUuzŽ=ˆ‰uwƒÚXŒ‰uy9zKŽ‡x^†|{

~u

†|w|‚

~v

9

~n T · ~u = 0 : 4n 1 − n 2 + 8n 3 = 0

~n T · ~v = 0 : 4n 1 + 3n 2 + 4n 3 = 0

‘?Ê)us‡ÈtusyMzF†|w|€uwݓ’s¼ŽC‚ƒŒ‰us/‡wKÉGuÚ^x^w|wKŽUuw˗*‚ƒu“:á†|{º}Kv€u“†+7uˆ’uswƒuawÝ썌‰uszƒusvŽUˆ‰€Œ9x^‚

€uÉGuw5ōr–x^ˆœÂ"È#šCzxTŽ=‚|su»ÂíKˆ‰†|w|€

ν −7

4 4

Å ã^z|u

~n = −7

4 4

Å

rtsvu>*uÚKŽU}Œ‰ÚuZŽ‰ŽUu»ˆµŽ‰uavŽ=ˆ‰syMz‚ƒu“:w?x^y9zCÊ=su»{º}Kv€^Ž=‚xWŒ!9

−−→ GH + −−→ HV + −−→ V U + −−→ U G = ~ 0

−−→ GH + µ~v + σ~n + λ~u = ~ 0 || · ~n T

~n T · −−→ GH + ~n T · µ~v

| {z }

=0

+~n T · σ~n + ~n | {z } T · λ~u

=0

= 0

~n T · −−→ GH + σ~n T · ~n = 0

r–xWŒ9x^†|ˆœ{º}Kv€^Ž

σ = − ~n T · −−→ GH

~n 2 = − 1 81

 − 7 4 4

 ·

 11

− 5 4

 = 1

r–xWŒ9x^†|ˆœ~ã^Ž=ˆ‰sy9z‚ƒuŒ„=É?ˆŽMx^w|‚‚ƒuŒ‡È‡uŒMxW‚|uw¥uŒU“:svŽµŽUuw=9

d(g, h) = | −−→ V U | = | σ~n | = 9

þ)Œ9x^†|y9zKŽ–“’x^w1wƒ}ƒy9z…‚|su+ƆwƒÚKŽUu

U

†|w|‚

V

—jˆ‰}¥ˆµuZŽUáZŽ–“’x^w

σ

†|w‚

~n

sw…‚|svuE*uÚKŽU}Œ‰ÚuZŽ‰ŽUu usw†w|‚víKˆµŽ=‚x^ˆuwKŽUˆµŽUuzƒuw‚ƒu#Â"È»š¥{ºŠƒŒ

µ

†|w|‚

λ

Å

KFLsx OQP=R+ST<UPV>bgy`yXzXZP\XZP|{~}>P_<P_

rtsvuaˆµuîuZŽ9zƒ}ƒ‚ƒuÉGuŒU†|zŽCx^†|{‡‚ƒuŒ’îí€KsyMzƒÚus¼Ža—-áa†êáZÊ)us)Ê=sw|‚|ˆUy9z|su{~uw4ÈtuŒ9x^‚ƒuwê€uawx^†

uswêÆxxWŒÁëGxTŒMxWvuavuŒ:•ÉGuwƒuawïáa†I?w|‚ƒuw5—swꂃuawƒuw

g

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h

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ȇuŒMxW‚|uwsˆŽ=‚?xWww¥€KusyMz‚ƒu“½„=ɍˆµŽMx^w|‚‚|uŒ•ÉGuwƒuawËÅ

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1

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h

ë?xWŒ9x^vuˈµ}Á덌‰}:µsvásuŒ‰uwCÚ^x^w|w5—ƒ‚x+‚svu–ˆ‰}ÁÚ}wˆŽUŒU†|suŒµŽUu#ȇuŒ9x^‚ƒu

h 0

ˆ‰sy9z¥“’s¼Ž

g

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U

É?s‚|uZŽ‚x^w|w”‚ƒuaw’„‡†|{ºë†|w|ÚKŽ uaswƒuŒ •ÉGuawƒu

E 1

ёj†|ˆ9x^“:“+uw’“’s¼Ž)‚ƒuw

˜sy9zKŽ9†|wƒ€Kˆ

Ã

uÚFŽU}^ŒUuw

~u

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~v

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(6)

E 1

E 2

Q Q Q Q

Q Q Q h Q

Q Q Q Q

Q Q QQ h 0

!! !! !! !! !! !! !!

g d(g, h)

G r r H 0 r H

U V

Q Q Q s ~v

!! ~u ! 3 6

~ n 0

6

„=É|ɍs‚†|wƒ€Cé9|Æ-xWŒ9x^vuu#•ÉGuwƒuw

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g

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‚|su:ȇuŒ9x^‚ƒu

h

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V

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Ã

uÚKŽU}Œ‰uwzxWÉGuaw˗ˆ‰sw|‚ˆUsvu»ë?xWŒ9x^vu¹—ˆ‰suzƒu#„=É|É?s‚†|wƒ€CéƒÅ

î…x^wêuŒUz?ã^¼Ž’uswƒuwÝÜ}ŒU“”x^vuw

Ã

uÚKŽU}Œ

~n

‚ƒuŒ’•ÉGuw|uw˗sw‚ƒu“Ù“’x^w䂍x^ˆ*uÚKŽU}Œ‰ë|ŒU}X‚†ƒÚKŽ

~u × ~v

‚ƒuŒœÉGuas‚ƒuaw˜sy9zKŽ9†|wƒ€Kˆ

Ã

uÚFŽU}^ŒUuw¥É?s‚ƒuZŽaōrtsvuˆ‰uŒ*uÚFŽU}^ŒsˆŽ{ºŒ‰us5swÉGus‚ƒuw•ÉGuawƒuw

Ã

uŒUˆ‰yMz|suÉ|É?xWŒÅXî x^w’ÚWx^ww”sz|wCˆµ}덐xTŽUásuŒ‰uw5—F‚?x#uŒ‚|†ƒŒUyMz”‚ƒuaw”„‡†|{ºë†|wƒÚFŽ

H

‚ƒuŒ)•ÉGuwƒu

E 2

ã^†{ŽaōšFuas

H 0

‚svutáa†|“ Ü}ŒU“”x^vuw

Ã

uÚKŽU}Œ)ë?xWŒ9x^vuavu–ÆŒ‰}@:RuÚFŽ9sv}Kw

Ã

}Kw

H

x^†|{

E 1

Ńr–x^w|w

ɍs‚|uw‚|su»Æ*†|w|ÚKŽUu

G, H 0

†|w‚

H

uaswŒ‰uyMzŽRÊ=swƒÚXsv€uˆ=r‡Œ‰usvuayUÚGÅ

î…x^wÚ^x^w|wˆUsy9z1wF†|wuaswƒu#€u}“:uZŽUŒUsˆUy9z|u#r‡u†ƒŽU†wƒ€C‚ƒuˆ<*uÚKŽU}Œ‰ëŒ‰}X‚†ƒÚKŽUuˆá†Ü‡†XŽUáu“’xTà

y9z|uwËÅ|r–x^ˆFuÚKŽU}Œ‰ë|Œ‰}ƒ‚|†|ÚKŽ

−−→ GH T · ~n = | −−→ GH | | ~n | cos( 6 −−→ GH ~n)

ˆŽUu¼Ž‚svu»Æ-Œ‰}@:RuÚKŽ9sv}Kw‚ƒuˆ

*uÚKŽU}ŒUˆ

−−→ GH

x^†|{ ‚|uwguÚFŽU}Œ

~n

“Á†|vŽ9sv덐sváasvuŒµŽ‡“:svŽ‚|uˆ‰ˆ‰uwÜ=}ŒU“

| ~n |

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=}F}ŒU‚swxTŽUuwˆßƒˆµŽUu“:ˆÁx^wƒ€uÉjuw˗

~n

xWÉGuŒuswƒu

Ã

xWŒ9sxWɍu¥Â ã^wƒ€uCzxTŽa—"sˆµŽÁuˆ#áÊ)uyUڃ“’ãKsv€—

‚|su=ƌ‰}@:RuÚFŽUs}Kw’w|sy9zKŽx^†|{

~n

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uÚ^}Œ

~ n 0

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*uÚKŽU}Œ‰ë|ŒU}X‚†ƒÚKŽ€u{º†w|‚ƒuw|uwguÚFŽU}Œwƒ}ƒy9z‚|†ƒŒUyMzˆµuswƒu»Ü=}ŒU“ Û¹ˆµuaswƒu# ã^w|€^uWގUusvuawËÅ

î…x^wêz?xaŽ’‚x^“:svŽ+uswƒuwꄇ†ˆ‰‚ƒŒU†yUÚG—-“:svŽ:‚ƒu“ ˆUsyMzê‚|svŒUuÚKŽ’‚ƒuŒ:„=ɍˆµŽMxWw‚ïáZÊ=sˆ‰yMzƒuwêáZÊ)us

Ê=sw‚|ˆ‰yMz|su{~uw…ȇuŒ9x^‚ƒuaw¥ÉGuˆµŽ9s“:“:uwã^Ž9

d(g, h) =

−−→ GH T · ~u × ~v

| ~u × ~v |

þ)uax^y9zKŽ‰u89rtsuþ)uZŽUŒ9xW€Kˆ‰ˆµŽ‰ŒUsy9z|uœs“(Üuaw|wƒuŒ*‚|uˆþ)ŒU†|y9z|uˆ-ÉGuáusy9z|w|uw:‚svuÜ=}ŒU“ uswƒuˆhuÚFà

ŽU}ŒUˆ—Ë‚svu:€Œ‰}@^uaw þ uZŽUŒ9xW€KˆUˆŽUŒUsyMzƒu:‚ƒuaw þ uŽ‰ŒMxT€uswƒuŒ‘Ëx^z|œÛgÉ|áÊ#Å˂|su:Ü=}ŒU“usw|uˆtuasw|‚s¼à

“+uaw|ˆ‰s}Kwx^vuawn*uÚKŽU}ŒUˆ9ÞMÅ

슃Œ†w|ˆµuŒþ)usˆ‰ësvuaËuŒ‰€KsÉƒŽ=ˆ‰sy9z‚x^w|w‚9

d(g, h) =

11 − 5 4

· 1 36

 − 28 16 16

 = 1

36 ( − 308 − 80 + 64) = 9

KFL„ƒ OQP=R+ST<UPV>{n…R+`P\[‡†BPa`pR+d_wRpPa`+ˆd‰lSd_YŠ^*_‹UPa`ŒW0_yXsˆ^Žˆ

rtsvu

Ã

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(7)

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g

ɍáZÊ#ÅGxW†{"‚ƒuŒtȇuŒMxW‚|uw

h

{ºŒ‰us

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λ

†w|‚

µ

9

d(g, h) =

(11 + 4µ − 4λ) 2 + ( − 5 + 3µ + λ) 2 + (4 + 4µ − 8λ) 2 1 2

rtsvu‡‚xWŒ‰€uˆŽUu¼ŽUu=ì?†|wƒÚFŽ9sv}Kw’ÉGuˆ‰yMzƒŒ‰usÉƒŽ usw|u=ìã^yMzƒu=s“›

3

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wxTŽUuw

λ

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ÉGuˆµŽ9s“:“:uwËÅ

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