若向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/0.png)
的夾角為120°,且
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/1.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/2.png)
,則有( )
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/3.png)
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/4.png)
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/5.png)
‖
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/6.png)
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_ST/7.png)
‖
【答案】
分析:由向量數量積公式計算
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_DA/0.png)
,即可得出選擇.
解答:解:由題意知
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_DA/1.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_DA/2.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_DA/3.png)
=1+1×2cos120°=0,
所以
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181001097779533/SYS201310241810010977795003_DA/4.png)
.
故選A.
點評:本題考查平面向量數量積的運算及兩向量垂直的條件.
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