问题
填空题
已知向量
|
答案
∵
+OA
+OB
=OC
，且|0
|=|OA
|=|OB
|=2，OC
∴向量
，OA
，OB
两两夹角均为120°OC
∴|
|2=|OA
|2=|OB
|2=4，OC
•OA
=OB
•OB
=OC
•OA
=-2OC
∴
•AB
+AP
•BC
+BP
•CA CP
=(
-OB
)•(OA
-OP
)+(OA
-OC
)•(OB
-OP
)+(OB
-OA
)•(OC
-OP
)OC
=（|
|2+|OA
|2+|OB
|2）-(OC
•OA
+OB
•OB
+OC
•OA
)OC
=12+6=18
故答案：18