问题
填空题
在正方体ABCD-A1B1C1D1中,点E在A1C1上,|A1E|=
|
答案
∵
=AB
,A1B1
= AD A1D1
∴
+AB
=AD
+A1B1
=A D1 A1C1
∴
= AE
+AA1 A1E
∵|A1E|=
|A1C1|1 4
∴
=AE
+AA1 1 4
=A1C1
+AA1 1 4
+AB 1 4
,,AD
∵
=xAE
+yAA1
+zAB AD
∴x=1,y=
,z=1 4 1 4
∴x+y+z=3 2
故答案为3 2