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解题方法
1 . 17世纪法国数学家费马在给朋友的一封信中曾提出一个关于三角形的有趣问题:在三角形所在平面内,求一点,使它到三角形每个顶点的距离之和最小.现已证明:在
中,若三个内角均小于
,则当点
满足
时,点
到三角形三个顶点的距离之和最小,点
被人们称为费马点.根据以上知识,已知
为平面内任意一个向量,
和
是平面内两个互相垂直的向量,且
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb1e439aee848fb6c75e7ecae6f91de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f408a1fdf7b0314b35cc80e96abba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753dde089c70db3820f7e3ea0d65d288.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2021高二·江苏·专题练习
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2 . 已知点
,直线
,且点P不在直线l上.
(1)求证:点P到直线l的距离
;
(2)当点
在函数
图像上时,(1)中的公式变为
,请参考该公式求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc26262f7a1603369462c7c2f2197a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3783208484c038053c9585a1040223a2.png)
(1)求证:点P到直线l的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bdc6a7931214e997187a9be2094a24.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc26262f7a1603369462c7c2f2197a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35ace358dac95dc2df0e8985c1eb041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a4bd8aa15b7501b0893988d31c68d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad2faff8fd7d3f1e37a9d074b2c8812.png)
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