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[RIȺ*=zdj NaturezaS   <(  < < 3 rId " -  > < aAND:\FRONTPAGE THEMES\NATURE\ANABNR2.PNG"P   < H`I "   > < 6@I " I s;Faa clique para editar o estilo do ttulo do modelo global<< < 0iI "  I v>Faa clique para editar o estilo do subttulo do modelo global?? < 6Hp` "` I X*  < 6(v` "  ` Z*  < 6y` "  ` Z* H < 0޽h ? [RIȺ*=zdj   P H 0  (    S XJ8P <$D 0  J <  TI ??p,$D 0 >Num eixo a posio de um ponto fica definida por um s nmero.?(2? ?B   `D??  ,$D 0B  ZD??P ,$D 0B   ZD??P ,$D 0B   ZD??P ,$D 0B   ZD??P ,$D 0   TDI ??`  ,$D  0 IA 20    TI ?? P p ,$D  0 E0 2   TI ?? p ,$D  0 E3 2   T0I ?? @ ,$D 0 Gx 2   TI ?? ,$D  0 N A 3 2  B   `D?? @ 0 ,$D 0    `LI ?? O ,$D  0 R"  "   H  0޽h ? [RIȺ*=zdj KC@(  J  Td_ ??p,$D 0 LNo plano a posio de um ponto fica definida por um par ordenado de nmeros.M(2M MB   `D?? p ,$D 0  Tl_ ??0 P,$D 0 Gy 2   TD_ ?? 0 ,$D 0 Gx 2   T4_ ?? @ 0 ,$D 0 E0 2 B    fD??0 @0 ,$D 0B    fD??0 @@ ,$D  0   Th_ ?? p ,$D  0 E2 2    T"_ ?? `0 ,$D  0 E3 2   T&_ ?? `0 ,$D  0 IA 2!    T`*_ ?? ,$D 0 UA ( 3 , 2 ) 2 B   `D??@ @,$D 0  T|-_ ??@ ,$D 0 `COORDENADAS NO PLANO(2,ff B   `D?? P ,$D 0   `1_ ??p  ,$D  0 R"  "   H  0޽h ? [RIȺ*=zdj  ^V(    S G8P<$D 0   M  TH ??,$D 0 ONo espao a posio de um ponto fica definida por um terno ordenado de nmeros.P(2P PW  TM ?? ,$D 0 YConsidera-se para isso um referencial cartesiano tridimensional, composto por trs eixos:Z(2Z Zp  T`` ??P p ,$D 0 :- Eixo Ox  Eixo das Abcissas4 2!&r  T` ?? p ,$D 0 <- Eixo Oy  Eixo das Ordenadas4 2!&j  T` ?? p7,$D 0 4- Eixo Oz  Eixo das Cotas4 2!&H  0޽h ? [RIȺ*=zdjq  !  P  (    T9_ ??,$D 0 Os trs eixos so perpendiculares dois a dois (referencial ortogonal) e considera-se a mesma unidade de comprimento nos trs eixos (referencial monomtrico).(2& B   `D?? ,$D 0B   `D??  ,$D 0B   `D??  ,$D 0B   fD?? ,$D 0B   fD?? P ,$D 0B   fD?? ,$D 0   T@_ ?? @ ,$D 0 Gz 2    T D_ ?? P ,$D  0 Gy 2    TH_ ?? p ,$D  0 Gx 2    T`K_ ?? P ,$D  0 E0 2 H  0޽h ? [RIȺ*=zdj#  ""4^"(    Z?? ,$D 0r   6Gq" p ,$D 0r  @ T>OG]p pP,$D 0 @  S Q8P <$D 0     TxS ?? &,$D 0 TOs trs eixos coordenados Ox, Oy e Oz definem trs planos, perpendiculares entre si:LU(20Z0k  Td` ??  ,$D 0  - plano xOy^ 2     &Z  T_ ??` = ,$D 0  - plano yOz X 2    ]  Tf ??   ,$D 0  - plano xOzP 2    &B @ ZD?? ,$D  0B  ZD??  ,$D  0B @ ZD??  ,$D  0B   fD?? p ,$D  0B   fD?? ,$D  0B   fD??   ,$D 0" "  0e0e BCDEFA5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?P @`  ,$D 0* #  0e0e BCDEF"A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@` p,$D 0" $  0e0e BC DEFA5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?   @` ,$D 0 &  0e0e BC`DEFA5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?``` @` @  ,$D 0B )@  fD!Ԕ?? P  ,$D 0B *  fD!Ԕ?? ,$D 0B +  fD!Ԕ??  ,$D 0 , Tp ??P `p ,$D 0 E0 2  - Tt ??p`,$D 0 Kz 2!  . Ts ??P p,$D 0 Kx 2!  / Tq ?? 0 ,$D 0 Ky 2! L 0 T ??  ,$D 0 ,Os planos dividem o espao em oito octantes.- 2# &#H  0޽h ? [RIȺ*=zdj  JB(    S 8<$D 0   B   `D??   ,$D 0B   `D?? ` ,$D 0B   `D?? P  ,$D 0B   fD??   ,$D 0B   fD?? `  ,$D 0B    fD??  ,$D 0   T܉ ??0,$D 0 Gz 2    TT ?? ,$D  0 Gy 2    T ??` @ ,$D  0 Gx 2    T ?? p ,$D  0 E0 2    `ԗ ?? p> ,$D  0 R"  "     T  ??P p ,$D  0 IA 2!   T ??@ p ` ,$D 0 E3 2    ` ??0,$D 0 R"  "      `t ??0 `. ,$D 0 R"  "     T ??` ,$D 0 F-4 2   T ??`,$D 0 F 4 2   Ṯ ??  ,$D 0 IB 2!   T` ??`,$D 0 IC 2!   T ??0P,$D 0 dA ( 3, 0, 0 )  2! B   `D??,$D 0  Tܼ ??0 ,$D 0 eB ( 0, -4, 0)   2! B   `D??0,$D 0  T ?? P@ ,$D 0 eC ( 0, 0, 4 )   2! B   `D?? 0  ,$D 0H  0޽h ? [RIȺ*=zdj  8(  "   0e0e BC DEF5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?   @`  ,$D  0"   0e0e BC DEF5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?   @` @` ,$D 0"    0e0e BC DEF5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?   @`@  ,$D 0r  S `8  ` B   `D?? @ ,$D 0B   `D??@  @ ,$D 0B   fD??@ ,$D 0B   fD??@ @ ,$D 0B   fD??0 @ ,$D 0   T_ ??,$D 0 Gz 2    T_ ?? ,$D  0 Gy 2    T0_ ??P,$D  0 Gx 2    TT"I ?? 0 ,$D  0 F 0 2    ` ` ?? m ,$D 0 R"  "      T(&` ?? = ,$D  0 R"  "      `#` ?? `. ,$D 0 R"  "   B   `D??@ ,$D 0B  # lD>??  ,$D 0  T(/` ?? P ,$D 0 b Plano x = -3& 2 B  # lD>??  ,$D 0  TP3` ??p P ,$D 0 a Plano x = 0& 2 B  # lD>??  ,$D 0  TD8` ?? P@,$D 0 a Plano x = 2& 2   T<` ??P ,$D 0 ^AO EIXO DAS ABCISSAS(2!   T@` ??0 p P ,$D 0 F-3 2   TD` ?? ` ,$D 0 E2 2 H  0޽h ? [RIȺ*=zdj /'`=(     TDR_ ??0,$D  0 Gz 2    TU_ ?? ,$D  0 Gy 2    TY_ ?? P,$D 0 Gx 2   Th]_ ??P0,$D 0 b Plano y = -3& 2 B  # lD>?? p ,$D 0  Ta_ ?? P ,$D 0 a Plano y = 4& 2 B  # lD>?? p ,$D 0  Tf_ ??` P ,$D 0 a Plano y = 0& 2   T|k_ ??P 0V,$D 0 _AO EIXO DAS ORDENADAS(2! r @ T>@o_G _ ,$D  0 @   `r_ ?? ^ ,$D  0 R"  "   r @ N>h_G ,$D 0 @   `z_ ??`. ,$D 0 R"  "   r @ N>T~_G.? ,$D 0 @   TL_ ?? ,$D 0 R"  "      T_ ??0 P ,$D  0 F 0 2   T`_ ??`  ,$D 0 F-3 2   T8_ ??` ` ,$D 0 E4 2 B   fD>??@   ,$D 0B   # lD>??p,$D 0B !  fD>?? ,$D 0B   `D??` p,$D 0B    fD??0 ` ,$D 0B   fD??` ` ,$D 0B   `D??`  ` ,$D 0B   fD??`  ,$D 0B   `D??@` ,$D 0 = 6_   PLANOS PERPENDICULARES AOS EIXOS!!$ !H  0޽h ? [RIȺ*=zdjF p (  r   `GV??  ,$D 0r   fGV??  ,$D 0  T_ ?? ,$D  0 Gz 2   Tx_ ??P p ,$D  0 Gy 2    Tp_ ??@`,$D 0 Gx 2    T$_ ??  ,$D 0 b Plano z = -3& 2 B   # lD>??0 ,$D 0   T_ ??Ppp,$D 0 a Plano z = 5& 2 B  # lD>??@  @ ,$D 0  T_ ??  ,$D 0 a Plano z = 0& 2   T8_ ??PP V,$D 0 [AO EIXO DAS COTAS(2!    `$_ ?? `. ,$D 0 R"  "     Th_ ??` p ,$D 0 F-3 2 B  # lD>??P  P ,$D 0r   `GV??  ,$D  0  T_ ??   ,$D  0 G 0 2 B   `D?? ,$D 0B   fD?? p,$D 0B   fD??  ,$D 0B   `D??  ,$D 0B    `D?? ,$D 0B   fD??p0 ,$D 0   ` _ ?? `.,$D  0 R"  "     T_ ??P p,$D 0 E5 2    T4_ ??0 `P ,$D 0 R"  "      6$_   PLANOS PERPENDICULARES AOS EIXOS!!$ !H  0޽h ? [RIȺ*=zdj4  %t(  r   `G9?? `,$D 0r @  fG??_ ,$D 0  Z??  ,$D 0  T@` ?? ` ,$D 0 H y 2   c $T`8p@<$D 0  ` 3  T` ??  ,$D 0 { - plano x=3@ 2    ;  T<` ??` = ,$D 0  - plano y=4H 2    C   T8` ??   ,$D 0  - plano z=6P 2     B @  fDԔ?? pp,$D  0B   fDԔ??ppp ,$D 0B   fDԔ?? p ,$D  0  T` ?? ` ,$D  0 E0 2   T` ??@ `,$D  0 Gz 2   T|` ??P p,$D  0 Gx 2 /  T` ?? ,$D  0 w)A interseco dos trs planos o ponto P* 2) *   `h` ??  ,$D 0 )3     `̷` ??  ,$D 0 )4  !  `` ?? T,$D  0 )6  "  `` ?? ,$D  0 R"  "((  #  `` ??p@ ,$D  0 )P B $  `D??``P`,$D0 %  f` ??,$D0 K(3,4,6) 2 H  0޽h ? [RIȺ*=zdj.  7./. 0=-(  r   `G ?? PP P ,$D 0r @  fG?? Q p,$D 0  Z??P P p,$D 0  T7I ?? @@,$D 0 H y 2   c $L:I8p <$D 0  I B  @  fDԔ?? ,$D  0B    fDԔ?? ,$D 0B    fDԔ??  ,$D  0   T8=I ?? @@,$D  0 E0 2   T,@I ??,$D  0 Gz 2   TCI ??0,$D  0 Gx 2 g  TGI ??P0V,$D 0 aIndique as coordenadas dos pontos A, B, C, D, E, F, G e H, do espao, vrtices do paraleleppedo.b 2a b   `MI ??ZFz,$D 0 )3    `PI ?? ,$D 0 )8    `TTI ??@` ,$D 0 )4    `$WI ??`  ,$D0 R"  "((    `\I ?? `_ ,$D 0 )A    `T_I ??@$ ,$D 0 R"  "((    `cI ?? ,$D 0 R"  "((    `$hI ??`  ,$D0 R"  "((    `0mI ??v 0,$D0 R"  "((    `\qI ??& ,$D0 R"  "((    `uI ??& @$ ,$D0 R"  "((     `LyI ??v 0,$D0 R"  "((  !  `8~I ?? ,$D 0 )B  "  `dI ?? t0 ,$D 0 )C  #  `pI ??  ,$D0 )D  $  `ԈI ?? `I,$D0 )E  %  `I ??  ,$D0 )F  &  `X>I ?? P O ,$D0 )G  '  `I ??@ `,$D0 )H  ( TI ?? ,$D 0 dA ( 3, 0, 4 )  2 B )  `D??@@,$D0 . TКI ??  ,$D 0 dB ( 0, 0, 4 )  2 B /  `D??0 0 ,$D0 0 TПI ??  ,$D 0 dC ( 0, 8, 4 )  2 B 1  `D??  ,$D0 3 TФI ??  ,$D 0 dD ( 3, 8, 4 )  2 B 4  `D??  ,$D0 5 TЩI ??p  ,$D  0 dE ( 3, 0, 0 )  2 B 6  `D??  ,$D!0 7 TI ??`  ,$D" 0 dF ( 0, 0, 0 )  2 B 8  `D??  ,$D#0 9 TtI ??P p,$D$ 0 dG ( 0, 8, 0 )  2 B :  `D??  ,$D%0 < TtI ??@ `,$D& 0 dH ( 3, 8, 0 )  2 B =  `D??,$D)0H  0޽h ? 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