问题 填空题
在正方体ABCD-A1B1C1D1中,点E在A1C1上,|A1E|=
1
4
|A1C1|且
AE
=x
AA1
+y
AB
+z
AD
,则x+y+z=______.
答案

AB
=
A1B1
AD
A1D1

AB
+
AD
=
A1B1
+
A D1
=
A1C1

AE
AA1
 +
A1E

∵|A1E|=

1
4
|A1C1|

AE
=
AA1
+
1
4
A1C1
=
AA1
+
1
4
AB
+
1
4
AD
,,

AE
=x
AA1
+y
AB
+z
AD

∴x=1,y=

1
4
,z=
1
4

x+y+z=

3
2

故答案为

3
2

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