1、 l :2007-04-02Te: 2(1968), 3, , 8E ?B) =.谈突破难以建系的立体几何问题阮灵东(E ?, 335101)ms |:O123.2-44 DS M :A cI|:0488-7395(2007)15-0019-02 I 8+ 5 ,Y$ = (A)(B), 8+ 5 !Bty“5, bWUS“/ %. , bWUS“y H, ?_ E % ;?、 # # 5. 4 5 _ M 4 % ?3YVQ ,s bW_ p 8+ 4y“nBt5( bW 5) R aZE./ , I.1 m, ABCD-A1 B1 C1 D1, H (1 , OA1 AB =60, A1
2、AD =45, DAB =90, p:m1 1)s LAB1A1 C ;2)LAB1 B1 D1 DB ;3)LAA1 B1D1 DB ;4)= A-BB1-D ?. !AB =a , AD =b , AA1 =c,5 a = b = c =1,ab =0, ac=12 ,bc = 22 .1)AB1 =a +c, A1 C =a +b-c, AB1 = (a +c)2 = 3 ,A1 C = (a +b-c)2 = 2- 2 ,AB1A1 C=(a +c)(a +b-c)= 22 .cos= AB1A1 C AB1 AC = 112-6 2.s LAB1A1 C arccos 112-6 2
3、.2) !n B1D1 DB , On =xa +yb+zc,nBB1 =0, nBD =0(xa +yb +zc)c=0,(xa +yb +zc)(b -a)=0 ,192007 M15 Y x + 2y +2z =0,x -y- 2-12 z =0 ,|z =1,x =- 22 ,y =1-2 22 ,z =1.n=- 22 a +1-2 22 b+c .AB1n =(a +c)(- 22 a+1-2 22 b+c)=1 -22 ,n = n2 = 7-4 22 .!AB1 B1 D1 DB ,5sin= AB1n AB1 n = 2 -121-12 2,=arcsin 2-121-12
4、2,LAB1 B1 D1DB arcsin 2 -121-12 2.3)yAA1 B1 D1 DB , AA1 B1 D1 DB A B1 D1 DB , T:d = AB1n n = 2 -17-4 2,AA1 B1 D1DB 2 -17-4 2.4) !m ABB1 , O !m =xa +yb+zc,ma =0, mc=0x+12 z=0 ,12 x+22 y+z=0 ,|z=1 , x=-12 ,y=-3 24 ,z=1.m =-12 a -3 24 b +c,1):B1 D1 DBBE_ n=- 22 a +1-2 22 b +c, V:cos= mn m n = 4- 242 -24 2 p= A-BB1-D ?4- 242-24 2. 5 4y“ f /, bW_ F P5 %, 8ZE :B |BFa , b ,c;=| bW _ _ VU; %.1i:T _ “1 p , L9 ,1 p _ # WCX. 5 pV A,NE R a, ? z) 4y“ 8+ 5,4.20 Y 2007 M15
