题目内容
如图,四面体ABCD中,G为△ABC的重心,
=2
,以{
,
,
}为基底,则
=______.
BE |
ED |
AB |
AC |
AD |
GE |
∵
=
+
,
=
,
=
(
+
),
=
+
,
=
,
=
-
,
=
,
=
-
.
∴
=
×
(
+
)+
(
-
)+
(
-
)=-
+
.
故答案为:-
+
.
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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