名校
解题方法
1 . 对于空间向量
,定义
,其中
表示x,y,z这三个数的最大值.
(1)已知
,
.
①直接写出
和
(用含
的式子表示);
②当
,写出
的最小值及此时
的值;
(2)设
,
,求证:
;
(3)在空间直角坐标系
中,
,
,
,点Q是
内部的动点,直接写出
的最小值(无需解答过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b303ef66609858e8ab234b6dabccba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e382f70d741ee01c165391ce980155d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4461408813c1476a8a8073c83b8989.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23056c429159c0198f865ff11972d8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e17d2355419564f6d9737295412b58c.png)
①直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9873960d64934875139754efbdfe951d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af5f843689a63bc176c2d2171b6a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53168695826b0a33a23067b76173c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780ef5119f58f853ce9dd2b9176ffdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778ae4468d857c229073875e0ee0ce31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6772fa3937b97d9ec3aec1ea2ea143b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95086cc97ef93f5166489b3bc47e1911.png)
(3)在空间直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32ab04dd852329d5918b177c199eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee736aec4313d04a5921ed7e5800b3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d04a00e46c1ffb335f73506041c66dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084fc7655647b596d07e80269d086e5a.png)
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