题目内容
（2012•长宁区二模）在△ABC中，M是BC的中点，AM=1，点P在AM上且满足
=-2
，则
•(
+
)等于（ ）
| PA |
| PM |
| PA |
| PB |
| PC |
分析：如图所示，由AM=1，点P在AM上且满足
=-2
，可得|
|=
|
|=
．由M是BC的中点，利用向量的平行四边形法则可得
+
=2
．进而即可得出
•(
+
)．
| PA |
| PM |
| PM |
| 1 |
| 3 |
| AM |
| 1 |
| 3 |
| PB |
| PC |
| PM |
| PA |
| PB |
| PC |
解答：解：如图所示，
∵AM=1，点P在AM上且满足
=-2
，∴|
|=
|
|=
．
∵M是BC的中点，∴
+
=2
．
∴
•(
+
)=-2
•2
=-4
2=-4×(
)2=-
．
故选D．
∵AM=1，点P在AM上且满足
| PA |
| PM |
| PM |
| 1 |
| 3 |
| AM |
| 1 |
| 3 |
∵M是BC的中点，∴
| PB |
| PC |
| PM |
∴
| PA |
| PB |
| PC |
| PM |
| PM |
| PM |
| 1 |
| 3 |
| 4 |
| 9 |
故选D．
点评：熟练掌握向量的平行四边形法则、数量积运算是解题的关键．
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