题目内容
如图，平行六面体ANCD-EFGH中，棱AB，AD，AE的长分别为3，4，5，∠EAD=∠EAB=∠DAB=120°，则AG的长为______．
因为其为平行六面体
所以
=
+
+
=
+
+
．
∴
2=(
+
+
)2
=
2+
2+
2+2
•
+2
•
+2
•
=32+42+52+2×3×4×cos120°+2×3×5×cos120°+2×4×5×cos120°
=50-12-15-20=3．
∴|
|=
．
故答案为：
．
所以
| AG |
| AB |
| BC |
| CG |
| AB |
| AD |
| AE |
∴
| AG |
| AB |
| AD |
| AE |
=
| AB |
| AD |
| AE |
| AB |
| AD |
| AB |
| AE |
| AD |
| AE |
=32+42+52+2×3×4×cos120°+2×3×5×cos120°+2×4×5×cos120°
=50-12-15-20=3．
∴|
| AG |
| 3 |
故答案为：
| 3 |
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