【答案】
分析:根据向量数量积的定义,可得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/0.png)
?|cos<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/1.png)
>|=1?非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/2.png)
的夹角为0或π?非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/3.png)
共线?存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/4.png)
,可判断A,B,由存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/5.png)
?非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/6.png)
同向或反向?
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/7.png)
或
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/8.png)
可判断C,D,进而得到答案.
解答:解:若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/9.png)
,则|cos<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/10.png)
>|=1,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/11.png)
的夹角为0或π,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/12.png)
共线,故存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/13.png)
,故A正确;
若存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/14.png)
,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/15.png)
共线,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/16.png)
的夹角为0或π,即|cos<
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/17.png)
>|=1,即
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/18.png)
,故B正确;
若
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/19.png)
,则非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/20.png)
的夹角为0,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/21.png)
同向,故存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/22.png)
,故C正确;
若存在实数t
,使得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/23.png)
,即非零向量向量
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/24.png)
同向或反向,则
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/25.png)
或
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103103314210949715/SYS201311031033142109497009_DA/26.png)
,故D不正确;
故选D
点评:本题以命题的真假判断为载体考查了向量共线的充要条件,其中熟练掌握向量共线的几种等价变形是解答的关键.