Аналитическая геометрия. Шурыгин В.В. - 30 стр.

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µw
i
e
i
) = pr
π
(λv
i
+µw
i
)e
i
= (λv
2
+µw
2
)e
2
+(λv
3
+µw
3
)e
3
= λ(v
2
e
2
+v
3
e
3
)+
µ(w
2
e
2
+ w
3
e
3
) = λ pr
π
(v) + µ pr
π
(w)
pr
`
a
`
` ↑
V
n
V
n
\ {0}
V
n
a ∼ b
a = λb λ > 0 V
n
V
n
\ {0}/∼ V
3
`
µwi ei ) = prπ (λv i +µwi )ei = (λv 2 +µw2 )e2 +(λv 3 +µw3 )e3 = λ(v 2 e2 +v 3 e3 )+
                                  =
µ(w2 e2 + w3 e3 ) = λ prπ (v) + µ prπ (w)
   5,67-:0),- L-16[b6*8/9 70,*M,-/8? -8-+36|*,09 pr =
   ϳTxwx™xXWxZ ¿ŸÀ ” ©ŽŠ’ŽžŒ¤Ž‰Š’ ¡Šžž”Ž ¢‘”Àž ŠŒŽº
                                                                `


žŒŠ”œÀ ¡£’œÀ¥ žŠ ŽžŸ ¡£’œÀ¥  ‰ŠžŠŠ¦ ¢ÉŒ‰ŒŠ”Š ŠªŠ Œ¢
ª”œÐ ”Š¢’Š»‘Ð ¡”‹ŽŒ¦§ ҏ¡”‹£À«Œ’ ”Ž‰žŠŠ’ ŠŒ ¢‘”Žž£
”£‰Œ¦ Žœ‹Ž”Š¦ ”Ž‰žŠ¥ ¡”‹ŽŒŽ ‰ŠžŠŠ©Š Š”¡ªŽž  ¡”‹ŽŒº
Ž’ ŠŒ§

                                              a           `
                            Ç0/= •`=
   ‡79 -+-[,6)*,09 -/0 +2L*; 0/.-7?[-b68? /0;b-7 ` ↑ =
   ð͵xñÍXW´Z •= —,82080b,- 9/,-* .-,980* ,6.36b7*,09\ 0/.-7?[2*;-*
b -.3*L*7*,00 -/0\ ;-|,- /7*L2J}0; -+36[-; O-3;670[-b68? L79 /72K
)69 .3-0[b-7?,-:- b*18-3,-:- .3-/836,/8b6 V ‚6\ [,6)08\ 0 L79 7J+-K
:- 6OO0,,-:- .3-/836,/8b6ƒ= €6 ;,-|*/8b* V \ {0} ,*,27*bN b*18-K
                                                      n


3-b .3-/836,/8b6 V bb*L*; -8,-I*,0* ~1b0b67*,8,-/80\ .-76:69 a ∼ b \
                                                      n


*/70 a = λb 0 λ > 0 = „-:L6 ¡”‹ŽŒŽ b V · ~8- ~7*;*,8 O618-3K
                      n


;,-|*/8b6 V \ {0}/∼ = { .3-/836,/8b* V /b-+-L,N b*18-3-b :*-;*8K
                                                      n


30)*/1-:- .3-/836,/8b6 16|LM 861-M 176// ~1b0b67*,8,-/80 /-L*3|08
               n                                  3


3-b,- -L0, ŽªŒŒ¤‘¦ ”Ž‰žŠ ‚861 ,6[b6J8 b*18-3 L70, *L0,0 6ƒ=
H-~8-;2 ;,-|*/8b- ,6.36b7*,0M b :*-;*830)*/1-; .3-/836,/8b* ,6N-L08K
/9 b- b[60;,--L,-[,6),-; /--8b*8/8b00 /- ;,-|*/8b-; *L0,0),N b*18-K
3-b= ¼/70 -87-|08? b/* *L0,0),* b*18-3 -8 -L,-M 8-)10\ 8- 0N 1-, 
-.0I28 /O*32 *L0,0),-:- 36L02/6= H-~8-;2 ;,-|*/8b- ,6.36b7*,0M b :*-K
;*830)*/1-; .3-/836,/8b* ,6N-L08/9 b- b[60;,--L,-[,6),-; /--8b*8/8b00
/- ;,-|*/8b-; 8-)*1 /O*3 *L0,0),-:- 36L02/6= 5,67-:0),; -+36[-;\
;,-|*/8b- ,6.36b7*,0M ,6 :*-;*830)*/1-M .7-/1-/80 ,6N-L08/9 b- b[60;K
,--L,-[,6),-; /--8b*8/8b00 /- ;,-|*/8b-; 8-)*1 -132|,-/80 *L0,0),-:-
36L02/6=
   ]= { /72)6* ,*-30*,803-b6,,-M .39;-M ` ‚.39;-M 70,00 b -+),-;
                                         –Ý

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