【答案】
分析:(1)當(dāng)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/0.png)
時(shí),求出向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/1.png)
、
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/2.png)
,利用數(shù)量積的坐標(biāo)運(yùn)算求出向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/3.png)
•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/4.png)
,從而求出向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/5.png)
、
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/6.png)
的夾角θ;(2)向量
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/7.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/8.png)
,代入函數(shù)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/9.png)
,利用三角函數(shù)的誘導(dǎo)公式進(jìn)行化簡,轉(zhuǎn)化為三角函數(shù)在定區(qū)間上的最值,即可求得結(jié)果.
解答:解:(1)當(dāng)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/10.png)
時(shí),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/11.png)
,
所以
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/12.png)
,
因而
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/13.png)
;
(2)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/14.png)
,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/15.png)
,
因?yàn)?img src="http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/16.png">,
所以
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/17.png)
,
當(dāng)λ>0時(shí),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/18.png)
,即
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/19.png)
,
當(dāng)λ<0時(shí),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/20.png)
,即
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/21.png)
,
所以
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182105713916433/SYS201310241821057139164019_DA/22.png)
.
點(diǎn)評:此題是個(gè)中檔題.考查向量的數(shù)量積的坐標(biāo)運(yùn)算以及向量的夾角,和三角函數(shù)的誘導(dǎo)公式和三角函數(shù)在定區(qū)間上的最值等基礎(chǔ)知識,同時(shí)也考查了學(xué)生靈活應(yīng)用知識分析解決問題的能力.