题目内容

如图,四面体ABCD中,G为△ABC的重心,
BE
=2
ED
,以{
AB
AC
AD
}
为基底,则
GE
=______.
GE
=
GM
+
ME
GM
=
1
3
AM
AM
=
1
2
(
AB
+
AC
)
ME
=
MB
+
BE
MB
=
1
2
CB
CB
=
AB
-
AC
BE
=
2
3
BD
BD
=
AD
-
AB

GE
=
1
3
×
1
2
(
AB
+
AC
)
+
1
2
(
AB
-
AC
)
+
2
3
(
AD
-
AB
)
=-
1
3
AC
+
2
3
AD

故答案为:-
1
3
.
AC
+
2
3
AD
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