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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