问题 填空题
在△ABC中,M是BC的中点,AM=1,点P在AM上且满足
AP
=2
PM
,则
PA
•(
PB
+
PC
)=______.
答案

M是BC的中点,

AP
=2
PM
,AM=1

PA
•(
PB
+
PC
)=
PA
•2
PM
=
PA
AP
=-(
PA
)2

=-(

2
3
MA
)2=-
4
9
.

故应填-

4
9

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