1、!*(!%!$%&9)+,-.256!l01&34!$!#$%#(#2$%&8#,0m(#.dmE-f0m#,.+Cp-qL2W-%!-2$FJ20FJ#,.($!%)*0/+*#/,*#.-*#/#!#!#!#$%&$#%#$&!%kl FJ,%$0.0&%$klFJ#,%$!%)*$0(0.%+*$(.%,*$0#.%-*$#.%$!#.4#&#$%&kl!%$#!%$&#%$0!%$!%)*$0!#%+*$!0#%,*$!%-*$.&%!#.!#$#$!-2 f(8#,.Em#,#.+$FJJ-#1FJ2,%$!%)*FJ+*#!FJ,*FJJ#,-*#!FJJ#,&!#&01#!#$%
2、&kl!%$#%$!%9!7$a*de$!%)*0槡!+*槡!,*0槡!槡!*-*!*)!#&4#2$!0%&.hkl4!-(!ekl!.vUu/k($klokl#W!%1#)%kl#oa*()W!%(1)#)&#klb*)o#kl#a*(W!%(1)#)b*()o#kl#kl#W!%(1)#!Ck+.kl#!gPhi4SSwe$k./*0$!%)*#+*!,*&-*.(!#$!#&#$%&kl!%$.%$&0!%4!7$+e,u#eKFJ#1 FJ%(FJK$(%!*!#-6#$#$%&kl!%$!#%$#0!%9!1)%$90/%$)&#%$0).(!#.01#/#!U#2$oFGa$K%
3、+%&$#%#$!&%,$&!%$%8#,Em27.$m%C4 FJK%FJ#1FJ),$)&#%!$#%9%)%!&FJK)$!%:$%;0)e.K(um#,GhiP$FJJK1 FJJK#1FJK,1 FJKde$!%)!FJK*+*!FJK*,*&FJK*-*.FJJK*$!%!#!#n#&$!kl!wkl(!1u!1!$a*(%!*78+!#$GH#*,p2#p2#_ FJK1FJK,%!FJK*#FJJK#1 FJK%!FJK*#_ FJK1FJK,1 FJJK#1 FJJK%.FJJK*#o|-!$F(!1b!1!#EGr3#HJ(!1%3!1!$!E 3%(#!3%#!#E3%(
4、%#!*9:+!$#%-!$!%#!#!jklm#9$8#,+#m.m(,9 FJ,#%!FJ,%!0%!%#%!$FJJ%$!%)!#&!0#&+*!&!0!&,*&!0&-*.!0.#!#.-67)i#$8K#./L.oeuKK#fe(!FJK%FJKFJK(%)FJK#)&#$#)1#.(!mngi.nqkl.e(kk.xH!+krklejk.tAkUSK(P0 x78EeQ0:Ee*.0mnnq./+d!;g-vCD-#,$#%klTJLumE+:UgPHV.fgklp.kl:kl,*v!$!%Bb:dkl,kle.%aU:E+e,-Em7%dh.FY&kl(u%&klUopa.klv
5、!A#;g+,-$#%kle.b78+SkletUjklJ;,-s(#$#%!#$-17i#($8#,+!FJJ#%!FJ,%.+(#(.+(Q,Q.+9($FJJ%$!%)*#!1#!+*#&!1!&,*!(!1.(-*.(!1!($!%!#&-6#$!-f08#,.m#,C.%#!#-%!&#,!9 FJ-%(#FJ#1(!FJ,$(#(!(a*%$(#1(!.(!*78+!#$#w#FJ%FJJ,1 FJ,%1 FJJQ#$FJ%FJ#1 FJJ#%!1 FJJQ0 FJJQ#%$1%#J!FJ%!10 FJQ#&5 FJJQ#%#!FJ(#%#!FJ#0 FJ($%#!0#!FJ$%#
6、Y&#J!FJ%!10#!0#!FJ$%#AJ FJ%!(!1.(!$F FJJ-%FJ#1 FJ#-%#!FJ#1!&FJ#,%#!FJ#1!&!FJ,0 FJ#$%!&FJJ,0#$FJ#5 FJ-%(#FJ#1(!FJ,#E(#%0#$#(!%!&!E(#1(!%#!*9:+!$#%,!$!%#!#./Ri#.$#,+%,#%!,*+f(,#,.+!9FJJ#%(FJ*1)FJJ+$(1)%!#!#.&h7CD#.$G8#,+*0#.+4 FJJ+%#!FJ+,#+u,*e-!FJ#%!FJ,%:fM!;klFJ-%!mnhkl.fg:.nqU/h($hklfg)%P.fM:hkl
7、fg78u;FJJ$P/#/0!mVv8#,)D FJ#FJ,FJ-$S|P Q(#$(!u=;g(H#$+,-./01$#%PfM:hklfg78;T+.uG9#%(!1)$()&#%$()%!hklFG.:0mnnqhkl./e,odJLFG:FG;aVno/g#/0!fgVmi*n!*78+!#$:;#J!0%!.#/$0!0#$%!#($!$F!b#E!7#E!=$%.$#E$%&!&$:;!yp?9y_pO!MSaV*?hYnono$CD!$#$QfP/!;gCD+,-./01$#%kljkFG(kl.FGWkl.eT:FGaBklk1*uD#:hoFGaWjk(*l!$!%!NFG
8、(kl.FG0:,*$9%&UkeS.FG$Hkl.FGvkN+N.:!$&%:a*a*(:FGkl.fM;P|HfMkl;.P7eFJ#%$!.%FJJ,%$#&%$FJJ%$!%)*$!.%+*$&(%,*$#%-*$0#0#%#!#&Ri#&$%&kl!%$#!%$%4!7$.($!%)*#+*!,*&-*.$!#$-17#$%&!%$槡&#%9kl0!FGq#!PLkl$.FG($!%)*$.%+*$!槡&0!%,*$0!槡&!%-*$!0!槡&%!#$(2iS#&$%&hkl%&.(*$4%槡&%!8#,+FJJ#%!%1!&FJ,%!%0$&(#,.+$FJJ%$!%)*!+*.,
9、*$-*/&!#$4&R2iS#($Poe-2 uum#,.Sm#fe-2S4e,eI+FJ-%!FJ#FJ2%#!FJFJI%(FJ,$(.($!%)*!9+*!(,*!-*!&!#.G7L#($%&b#,$0F#F,F%.m(#-0#C.x$u#/#%G-0 FJJ,.0$!%)*#+*#!,*-*0#(!#$(2CD#9$9*08#,Ghi.P456&FJ*0 FJ#0 FJ,%$8#*u8#,.hEO%de$!%)*&.+*#.,*#&-*#!)!#&Ri#($(&89.y*%$%.S/(#*$%0$%CP+$%(81$#0(%9$(&#%kl FJK+%(FJK1$#0(%FJK#9
10、wdx FJ*+#C7:$y*$%&89C.Ced-/!9y*%$1#$&#!C.Ced-/$a*C.12($!%)*&14%+*%,*&!0槡!14&%-*&!1槡!14&%*!#37R2J#&$hiE/kl!%$&!%$0#!%#%$.#%9!%1)#$)0 0umFJ#%$#0!%FJJ%$!#%$FJJ0FJ,%$!%)*+*.,*&-*!&!#01#/#2$hkl!_ax+w!7:!.0$!%)*!0#!+*!0#!0,*$!1%!%!1!-*$!1%0$!0%!0!#&3(#(#2$%&$0#%#$#!%,$0!0#%$&.%$kl FJ#FJ,kC.($!%)*&槡!+*
11、&槡#!,*0&槡!-*0&槡#!(!#$()#9#$%&kl!%$#槡&%$槡&#%$!u.(!)!#$&#&#$%&kl!%$#0#%$0.%!9!9$3!1%$a*3.(!*!#$!#&#$!kl!%$1#%$#!%4!9$%!#3(#$%&kl FJK9 FJ#FJK%&$FJK0FJJK#%!#,-#$%&)#)!0h#kl4)#0)!%#!9 h k l 5 60)#%0)!%#$%!#!#.-1#!#2$%&#kl)#)!.(45%#&9kl!%&)#0!)!$!%!$!#./#2$8#,0m(!.dmE%&kl!56 FJJ#%!FJ,%!1$_+bc.0!$VHGUbc
12、.%$!(#kl)%(#kl)&!9)7FJJ#,)($.!1%9 FJ#,*!2&$#%!#89#($!%$#!%$#%#%!1C!99#$a*C.de$!%)*0&!+*0&,*&-*&!$!%!#.&#($%&kl!%$#槡&%$&%9kl!.(*$a*%$!%)*!槡&+*槡&,*-*0槡&*78+!#$!%!#!$#%!#$#%!1C%!#1C#!1C$#I9#J#%#1C1!1C%#EC%0&!$F!%!#槡&$#%!&#$#E!%!#%91槡!#!%&1槡&*$#s&1槡&!=91槡!%槡&!#s&1槡&%槡&=91槡!#AJ?#/0!CD5+!$,%!*!$cnf$P/%!0!
13、$s x%!9;!0%d&hkl.*lE:vU,o.jk!$!%*lEewe.Skl.(*lEdewe*.!#!#!#&-1#!$)#)!(#kl4)#)!.(*&9!%)#1&)!%!)#$kl!kC.(!$!#&#$%&kl FJ#u FJ,.(#!P4FJJ#%&FJ,%!9FJ%(FJ#1 FJJ,4 FJ9FJ#,$a*(.(!两向量的夹角为直角*lEe4SklweSkl.(!$&%eFG.!%$#%#%$!%!%$!9;$#$!1%#%!%!54!5%$#$!1%#%!$!#1%槡!#0$!1%槡!kl120&*!2,-s(#$#%!#$jwRi#$9!#2(#kl4!0%$!0#
14、%0$0#%#$!10#.($!%)*槡!0#!+*#!,*槡!-*!$!%!#.3(#!$9kl FJK%$#0&%FJK%FJK#FJK0 FJK#%$FJ#%!*78+!#$R!E$&K?!%#%#!%#_!1!%!1!1!%!#o!1%槡!Q!0#$!0#$#J!0!1$#1#!#s0!1$#1#n#J!1$#3#!10#!%!1$!0!1$#1#!%&0!1$#_&0!1$#&0!=#%#!_!10#!#s!10#!:;$&:;!#?:;pR#%!1)!I#%#s!1)%#J!$!1!)$!1!)!%#IGH#!%#!%!n#J!1)!%#!0#%!#0$!0)#0#%0!1!#0)
15、$#oI!0#$!0#$#J.!#0$!0)-.0!1!#0)$-#Q#J!0#$!1)!)0#$!#s!01)!0)#5!1)!%#o1)3#!10#%!#0$!1!#0)$#o!10#!%.!#0$!1!#0)$-!%!#0$!1!#0$!#0)$!1!#0)$!%!#0$!1!#0)$!%!1)!0!1)$1!%&0!1)$!51)3#_&0!1)$#!o!10#!#s!10#!L!$&K?!%#!%#_/!#0%*!FJK%!#FJK#%#FJK,%#K?!9#_K9K#!UK#K#_p?$#%9y_O#!%!#$#%!#$#!#$#!#$!,!$#%$#%!$#%$#$!1%!%#!
16、0#%!#0$#0%$#0#%!0$#0%$#oI!0#$!0#$#J!#0$=!0$1!0%$=!#0%$#n#J#0$0%#s$1%3#!10#%!#0$#0%$#!10#%!#0$!1!#0%$槡!%&0!$1%槡$!K?$1%3#_&0!$1%$#s!10#!_!10#pj?#!$R&FJJK#%!$#%$#IFJJK%FJJK#$!1%槡!%槡#5 FJK FJJK#%$0&%#AJ$%&#%#a$%0&#%0#!:*lExy*0kl*lE./:mn+tkk.xHXUuEy*vd&z7#nq+d!k$#%P(R!ST#RN$!ST#%槡!N$!S%!T!$!S%0#S#槡JKKKKK
17、!N!N#!N#4!0NJKKK$!T#%0$T#%#JFJJQ(E(!%#%#!0%F:hoFGa!FJK,%$%Fkl.FG;(A:%&78Gjk.aUjkvA;g-9:$#%sx(:!%!0槡!$!?%!%!?!01!Fkl.(*lE!$!%(:kl.:kl.um$E$Hkl:6dv*!$!:*%&#%#;#FJ#槡%!%:$%0&#%0#;#FJJ#槡%!#FJ#%槡!&IH#FJ#FJK#FJJK#?ppSp#_FJJ#槡%!*9:+!$#%+!$!%槡!#.,-#9$!(S/jkl!.%&a*313!.(#!$!%)*9c$!Pc+*9c$Pc,*9!c$Pc-*9c$PcA;g-
18、&UV-9:$#%*(FG.;7=/l.y*:.v!$!%$*#%(G.;.#x;.v!$&%wdx(vk#$:wdx!0#!?#!1*$!%!#$)Ri#.$%&kl!%$#)%$0#)%9!0uo$)!.($!%)*#+*!,*&-*.#!#7CD#$%&!%#%$!0$0!%!$kl!u.($!%)*!+*&,*.-*$!#89jk#$%&kl!56!%#%!4!kC.u!kC.d$!0de$!%)*#+*槡&,*槡-*&%!#$7CD#$%&kl!0u#kl($P.kl$.ba*33!0.0$!%)*+*#!,*槡&!-*#&!#$Ri#$8#,+%&FJ#1 FJ,%FJ#0FJ,#
19、%!,%#-2(m#,.Ed$FJ-0FJ2%$!%)*/9+*#9,*!9-*!$9!#$(2CD#/$%&jkl FJK%!FJK#%4#,9K,(69 FJK,%(!$(-%$(de$!%)*!0!+*!0!,*!0!-*!0(!#(NOP#$9!#2(#kl4!0%$!10#.($!%)*槡!0#+*#,*槡!1#-*槡!)!#37j2J#!$GdoEK#+K%K#%#FJ#%.FJ,$FJJK,0$FJK#0 FJK%!*!#&PRi#&$%&FJK%#FJK#%槡!FJK0FJJK#%,HK#iHK,%.P!FJJK,%FJK1)FJK#$)&#%$%u%$0#!5%o$5!de$
20、!%)*槡!+*#!,*-*0#$!#&()#.#$K(mK#(e.+FJK%$0&#%FJK#%$0!C%$a*C%!%!#$%#$d#,+%,#%!#,%#H#,%$P!-2 fe#,C4 FJ#-%!&FJ#,FJ2%#$FJJ,$FJ-0 FJ2.(!&!#!#!#2$#,+m#.f(!#!9*+f0m#,C.456FJ#*FJJ#,%FJ,+FJ,$FJ*0 FJ+.120!#-6#.#5$!kl!C%5C*$AC*$%$C*%!%!#!-#!%$G#CN$!C0!C1#%.(!(!#&#(#!U#2$!kl!%$槡&A$A$A+%#H#%$P-(,.+!9 FJ,0 F
21、JJ#-%#$#.(!$!%!#.$%#&$%&#,.m(!H#%#!P-2 fm#,C#,%&#-,%(2!9 FJ-0 FJJ2%#$(.(!*78+!#$#FJ#-%0#!FJJ#1 FJ!K?FJ,FJ#-%#_!FJ#1 FJJ$0#!FJ#1 FJJ$%#s FJ!1#!FJ#FJJ0#!FJ#!%#!$K?FJ%#H#%$P#_ FJ#FJ%#!FJ#K$?#1#.FJ#0#!FJ#!%#!AJFJJ#%!$aFJ#%#!#_#p?#!*9#*!I%#H#%$P#*%#!#*%槡&!#%!)$#!#$#,#!#槡&$%!K?-,p2#_-!1#!#槡&$%!_ FJ#-%#!0#
22、!#槡&$%!#FJ,%1#!#槡&$%!I FJ,FJ#-%#J 1#$%!#!0#!$%1&.%#s!0%#_%!$a%FJ#FJ5#!P%!=!=0#$%!%0!#,2#FJJ#%FJ,#FJ%FJ#,#_ FJ-%FJ#1 FJ#-%FJ#1#&FJJ#FJJ2%FJ1 FJ2%#(FJ#1 FJJ#FJ-FJ2%FJ#1#&FJJ$%#(FJ#1 FJ$%.(1.&0!#1#&$%(%#AJ(%!*9:+!$#%#!$!%!#&89#$um#,+FJ,%$#!%FJ#%$0.hklh+.7#:FG0fg.Whkl.FGZ0#$.fl!vZLjkeklhklfg:n:P|k,kH!/0
23、!#fg(DFJ#FJFJ,$FJ#-FFJ,*FJ#-%#KFJ#fF/fKu8fg9(eN$#vhie$*hYnoFFJ#%noe!$FDnoF FJ,*FJ#-%#KfF/fKu8/0!a FJ2$FJ-D FJ#$FJQ&$4D=/cde(fP/!u;g#$=+,-9:$#%:hukl.a:kl;A#A15#A1A15#%#A1A%5!*0#$!I(#(*#J(*0#(*#5(*#o%*0#!YA1A#%#JA%AA%&%$槡!0A%9%1&%!$de!Ey*#hklP:nq0nqhkl.*lEFG:Ey*x;noM!1%#Q$PQ$#Y=?$P$#!;gm7=&+,-nm#,01$#
24、%kl(=nqEy*.7#:krkl.FGHEy*VnqUEy*.,#,dEy*jkU*nqL.!$!%eEy*jkP|USKx(PK07%A$&$1%.x3 P K 0 7%8A!$19A!$195$1:.x*!%)!#&hi#.$hum#,+FJJ#1 FJ,%($FJ#0 FJJ%0 FJ,%$um#,0$!%)*+*b,*-*#!#(NOP#.$8#,+#%&,%!FJJ#%#!FJ#,$FJ0 FJ#.($!%)*0!+*!,*0.-*.$!#$,-#/$%&kl!%$5A#A+#%!%#H%$P*#mC4*%#&#$FJ*0 FJ#de$!%)*0槡&!+*槡&!,*0#-*#!#
25、$7#$8#,+!FJ,!0FJ#!%!FJ*0FJJ#,x*.lmc8#,.$!%)*+*i,*-*/(!#$./G7#($G m(!.(#-0 CP$FJ-0FJJ,-.($!%)*#1!槡!+*0#0!槡!,*#0槡!-*#0!槡*!)!#./3Ri#.$oE#,+H,#%9P,%#,%!0nm#C.P/Ed$FJ,0FJ,#1 FJ,0 FJ,%!*!#$3(Ri#(#!U$%&kl%!A&$槡0&%$&)%y*$%0&.S7.(*!$#%y*$%.#vw)$!%$&0*$*&#!$%.!#$2i#(#!U$8#,.i#,G.mf(89:%&kl%$5槡&A0!5%0&%0#!$#%9
26、8槡%!&:%!8#,.hE)$!%90!:85*&1$%,.*!#!256!l01&34!;g-vCD;gCDHI:&9ICDdj2wlJ#$!1%1!%!#H$!1#1#%!11#u!LJRwl0JJ!LJ!0%!10#6;6(Lwl!JJ#(!%(!%!#m()n!(!L!JwR%m(n!(!L!JwR%m(%n!(!%(#H$()!#%()!%)(!#%!#1$(1)#!%(!1)!%&#$(!1#%(!1(#!;g-2HHvwH$#%(!0P/jkl9oP/a*(W%(!$klu!e$!%(9klujkl!e$oPP/a*(W%(!$&%#,0hCE4 u#w/#0hiP9,oe#C
27、$oa*(W FJ,%FJ1(FJ#$G%!$!=;g(H$#%hklfg)#)!0gPhi.S/wekleZPhi.kl!U4UPa*(#(!W!%(#)#1(!)!+)#)!0PfM!$!%hklfg.ahklfgB:%&kl;$#%!%$#%#%$!%!%$!7.b78($#%!0$!%#%!$!%E$#%#%#$!%!%,$&%&%e.b*78!(!($!0$#%$%&0%#%0$&0$#%$%!0%#%!7pEx$#$!%#%!#K?$!#%!Q!$!%!9;!0%!$&%!ugk!0%!)!uk!0%0!f.!0!%!%!0槡!$.%5%!0!$%!0#!#!=;g=g-y!%$#
28、%#%$!%!%!.($!$#%!0%$#$!1%#%!$!%!%$!#1%槡!#!9$#%#%#$!%!%$FJ#%$#0$!%!1$%#0%!%槡!$&%5%$#$!1%#%!$!#1%槡!#0$!1%槡!$.%!9;!0%;$#$!1%#%!%!$#%!0$!%#%b$#$!1%#%!%E6#2:;!%!$#%#$#%!$!#%!$p#2p!$!A=;g-X$#%!%!0!%!%!0槡!%!槡!)$!%!?%$!?%槡!%!?!01槡!)$&%9!%$%$!%$!1%槡!%!?R_$#%!0#!?#!1!$!%!1!1!0!%!$!1!%!f!2%s(!=;gs-u$#%ejkt:kl$
29、e%.b78(!7;!%(;$#%!0$!%#%$-(%!$!%ojkt:klo.b78(!9;!0%;$#$!1%#%!%!$&%jkt:sx(5%!0!%$#$!1%#%!$!#1%槡!#0$!1%槡!$.%e.:kl.ekl.!%!0槡!%$!1%槡!#%FJJ#%$!0$#%!1$%!0%#%槡!#!=;g7=s-uuEy*#nqkl.*lE.FG:0mnjk!vLjkBkl*lE.FGsx,kl,.FGsxEd.&z*!%!#!gh$#kk%!#.jklm#$%&!(#kl($P$!0%0%$!%)*0#+*,*#-*!#!#.!#.$!kl!56!1%槡#!0%槡$!0%$!%)*
30、#+*!,*&-*$!#7QR#!$8#,+FJJ#%!FJ#,%4!0($8#,($!%)*E+*oE,*E-*wJc%!#&2i#$%&kl!%$槡&#%$#%#%$C槡&%9!1!u#o$C%$!%)*0&+*0!,*#-*0#&!#$./&iS#$%&!%$%&!0%0#!$kl!klkC.($!%)*0.+*.,*0!-*!#42&Ri#9$G9FJK,%$FJK1%FJK#$!%)*($1%(#+*$1%)#,*$1%(0#-*0#($1%(!#&Ri#9$%&;2w(j.*_!8)#kl#)%$8)8)1#%)%$)1#%)&5 _k+.k0$!%)*9)&5 U#)7)7:$*
31、_!8)#0dt*_+*9)&5 U#)7)7:$*_!8)#0d%*_,*9)&5 U#)9)7:$*_!8)#0dt*_-*9)&5 U#)9)7:$*_!8)#0d%*_)!#!4#$S/j.hkl!Q%!00$9S/j.hkl!56!u.*&!)!*.*$%!4!QQ!T#&!&!#!+$!Q%$!%)*!+*&!,*#-*#!*!#.$%n#/$%&#,.m(!H#%#!P-2 fm#,C#-%(#,2%),!9FJJ-0 FJJ2%#FJ,-0FJ,2%0!&$(1)%$!%)*#!+*!&,*$-*(#!#&37#/$%&!0#kl!0%!9kl#56#0!0%#$#.($!%槡
32、槡槡槡)*!0#+*!,*!1#-*!1!e!ij$.kk!%!#3(#$Ri#$!kl!56!%#!0%0#!$!1!%!#!#!()#&$%&b#,.m(#-0#mC.x$FJ-0 FJ,#.()FJ-0 FJ,.(!$!#.*+#.$hkl!%$#!%$.!%#%!1$&#%4#u!.d e#u.$%!%!#$*+x4iS#$K 0hCP#,0hC8#,.E/H#H,f0m,#.!kbc.0!$x 56 FJK%FJK1 FJ#1 FJ,$8#,.P5678.#+)%x 5 6 FJJK%FJK1(FJ#FJ#1FJ,FJ,$%$()%$8#,.iP5678.#+)&x 56 FJJK%
33、FJK1(FJ#FJ#A#1FJ,FJJ,A#1FJJ,FJ,5$%,$()%$8#,.P5678.#+!f!79$.k%&!#!U$!#$7Ri#($%&$0!.%#$&0#%,$0&0.%!FJ#%!FJ#,%FJ,%#4 FJ,*%&#FJ,+%0!$#%&!10&#)$!%56!%1)#.a*0#,mC.mkl FJ.FG)$!%9-$CW8#,-(E4H#-,(-FG.12!(!#!U$!#7i#($%&kl FJK%$(5(A%$(-%FJK#%$0A#%+K(FG!$#%90#%*$4(%#kl FJKu FJK#.)$!%9FJ#3!FJK#a*#T7:a*(.12!)!#.U$!#./C%CD#($%&!%$#%kl!u.(&*.4!0%0#!$#%kl)$!%9 k l u k l(%$#%.(*!k l%5!5!,$%!+,(8#,.i41,%!*&1.*!
