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1、1Ùþê§1þ5$1.Xã,®²18¡NABCD−A1B1C1D1,E!F©O´cBC!−−→−→−−→−→−−→−→−→−→−→C1D1¥:.AB=a,AD=b,AA1=c.Á^a,b,cL«eþ:−−→−−→−→−−→(1)AC1;(2)BD1;(3)AF;(4)EF.D1FC1A1B1−→Dc−→CbEA−→aB11Kã):(1)Ï−−→−−→−−→−−→−−→−−→−−→−−→BC=AD,CC1=AA1,AC1=AB+BC+CC1,¤±−−→−→−→−→AC1=a+b+c.−−→−−→−−→(2)ÏBD1=BD+DD1,−−→−−→−−→−→−→−−→−−→BD=AD−AB=b
2、−a,DD1=AA1.¤±−−→−→−→−→BD1=b−a+c.−→−−→−−→−−→(3)AF=AD+DD1+D1F,−−→−−→−−→1−−−→1−−→DD1=AA1,D1F=D1C1=AB,22·2·1Ùþꤱ−→1−→−→−→AF=a+b+c.2−−→−→−→−→−−→−−→−→−−→−−→(4)EF=AF−AE=AF−(AB+BE)=AF−(AB+BE)=−→−−→1−−→1−→−→−→−→1−→1−→1−→−→AF−AB+BC=a+b+c−a−b=−a+b+c.22222−→−→−−→2.®²1o>/ABCDéACÚBD.AC=a,BD=−→−−→−−→−−→b.¦AB
3、,CD,DA.):Xã,−−→−→−−→1−→1−−→1−→−→AB=AO+OB=AC+DB=(a−b),222−−→−−→1−→−→CD=−AB=−(a−b),2−−→−−→−→−−→1−→−→DA=−AD=−(AO+OD)=−(a+b).2CDCOABAMNB12Kã13Kã−→−→−−→3.3△ABC¥,:M,N´AB>þn ©:.CA=a,CB=−→−−→−−→b.¦CM,CN.):Xã,Ï−−→1−−→−−→2−−→AM=AB,AN=AB,33¤±−−→−→−−→−→1−−→−→1−−→−→1−→2−→CM=CA+AM=CA+AB=CA+(CB−CA)=b+a,3333−−→−→
4、−−→−→2−−→−→2−−→−→2−→1−→CN=CA+AN=CA+AB=CA+(CB−CA)=b+a.33334.L,M,N©O´△ABCn>BC,CA,AB¥:.y²n¥−→−−→−−→þAL,BM,CN±¤n/.§1þ5$·3·−→−−→−−→y²:ÏAL,BM,CN±¤n/,=òùnþÚ"þ.d−→1−−→−→−−→1−−→−−→−−→1−→−−→AL=(AB+AC),BM=(BA+BC),CN=(CA+CB),222−→−−→−−→:AL+BM+CN=0.AANMNMOBLCBLC14Kã15Kã5.O´△ABC%,y²:−→−−→−−→OA+OB+OC=
5、0.−→):Xã,AL,BM,CN´3^¥,O´n/%.KOA=2−→2−→−−→2−−→−−→2−−→LA=−AL,OB=−BM,OC=−CN,Ïdd14K,3333−→−−→−−→2−→−−→−−→OA+OB+OC=−(AL+BM+CN)=0.3−→−−→−−→6.3o¡NO−ABC¥,:G´△ABC%.^OA,OB,OC5−−→L«þOG.−−→−→−→−−→−−→−−→−−→−−→−−→):ÏGO=GA+AO,GO=GB+BO,GO=GC+CO.d1−→−−→−−→5KGA+GB+GC=0.Ïd−−→−→−−→−−→3GO=AO+BO+CO.−−→1−→−−→−−→OG=(O
6、A+OB+OC).3−−→−→−−→−→−→7.ABCDEF8>/,¦AB+AC+AD+AE+AF.−−→−→−→−→−−→−−→−→−−→−→−→):ÏAD=AC+AF=AE+AB,¤±AB+AC+AD+AE+AF=−−→3AD.·4·1ÙþêFEOCADAGBBC16Kã17Kã−−→−→−→−−→−→−→−−→8.3o>/ABCD¥,AB=a+2b,BC=−4a−b,CD=−→−→−→−→−5a−3b(a,b´Ø"þ).y²ABCDF/.−−→−−→−−→−−→−→−→−−→−−→−−→y²:ÏAD=AB+BC+CD=−8a−2b=2BC,¤±AD//BC.−−→−−→
7、AD
8、
9、=2
10、BC
11、,¤±ABCD´F/.9.A,B,C,D´o¡Noº:,M,N©O´>AB,CD¥:.y²:−−→1−−→−−→MN=(AD+BC).2y²:Xã,−−→1−→−−→−−→1−−→CM=(CA+CB),CN=CD,22¤±−−→−−→−−→1−−→1−→−−→1−−→−−→MN=CN−CM=CD−(CA+CB)=(AD+BC).222ADCMbDbOBbNMABC110Kã19K
