题目内容
平面上的向量
，
满足
2+
2=4，且
•
=0，若向量
=
+
，则|
|的最大值为（ ）
| PA |
| PB |
| PA |
| PB |
| PA |
| PB |
| PC |
| 1 |
| 3 |
| PA |
| 2 |
| 3 |
| PB |
| PC |
A．
| B．
| C．
| D．
|
∵
=
+
，
2+
2=4，且
•
=0，
∴|
|2=
2+
2+
•
=
2+
2
=
-
2≤
∴当
=
时，
|
|的最大值为
故选C
| PC |
| 1 |
| 3 |
| PA |
| 2 |
| 3 |
| PB |
| PA |
| PB |
| PA |
| PB |
∴|
| PC |
| 1 |
| 9 |
| PA |
| 4 |
| 9 |
| PB |
| 4 |
| 9 |
| PA |
| PB |
=
| 1 |
| 9 |
| PA |
| 4 |
| 9 |
| PB |
=
| 16 |
| 9 |
| 3 |
| 9 |
| PA |
| 16 |
| 9 |
∴当
| PA |
| 0 |
|
| PC |
| 4 |
| 3 |
故选C
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