設(shè)兩個非零向量
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051748985305.png)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
不共線.
(1) 如果
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749016392.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051748985305.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749063385.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749078493.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749109387.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749125437.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
,求證:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749156300.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749172309.png)
、
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749172315.png)
三點共線;
(2) 若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749187321.png)
=2,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749203358.png)
=3,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051748985305.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
的夾角為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749250388.png)
,是否存在實數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749265339.png)
,使得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749265339.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051748985305.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749515347.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749531321.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
垂直?并說明理由.
(1) 證明見解析; (2) 存在實數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749562440.png)
,使得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749265339.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051748985305.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749515347.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749531321.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824051749000334.png)
垂直.
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