试题分析:不妨记以A为起点,其余顶点为终点的向量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755855645.png)
分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755871319.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755886321.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755902320.png)
,以C为起点,其余顶点为终点的向量
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755917618.png)
分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755917316.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755933329.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755949316.png)
.如图建立坐标系.
(1)当i=1,j=2,k=1,l=2时,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755964921.png)
=[(1,0)+(1,1)]•[((﹣1,0)+(﹣1,﹣1)]=﹣5;
(2)当i=1,j=2,k=1,l=3时,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755980922.png)
=[(1,0)+(1,1)]•[((﹣1,0)+(0,﹣1)]=﹣3;
(3)当i=1,j=2,k=2,l=3时,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755980922.png)
=[(1,0)+(1,1)]•[((﹣1,﹣1)+(0,﹣1)]=﹣4;
(4)当i=1,j=3,k=1,l=2时,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755980922.png)
=[(1,0)+(0,1)]•[((﹣1,0)+(﹣1,﹣1)]=﹣3;
同样地,当i,j,k,l取其它值时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015755980922.png)
=﹣5,﹣4,或﹣3.
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015756073922.png)
的最小值是﹣5.
故答案为:﹣5.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240157560894336.png)
点评:本小题主要考查平面向量坐标表示、平面向量数量积的运算等基本知识,考查考查分类讨论、化归以及数形结合等数学思想方法,考查分析问题、解决问题的能力