【答案】
分析:欲求|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/0.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/1.png)
|,一是設(shè)出
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/2.png)
、b的坐標(biāo)求,二是直接根據(jù)向量模計算.對于解法一,我們可以設(shè)出兩個向量的坐標(biāo),然后根據(jù)已知條件中|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/3.png)
|=1,|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/4.png)
|=2,|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/5.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/6.png)
|=2,對|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/7.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/8.png)
|的平方進(jìn)行化簡求值,進(jìn)而給出|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/9.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/10.png)
|的值.本題中沒有給出向量的坐標(biāo),故也可根據(jù)向量的平方等于向量模的平方進(jìn)行求解.
解答:解:法一:設(shè)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/11.png)
=(x
1,y
1),
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/12.png)
=(x
2,y
2),則x
12+y
12=1,x
22+y
22=4,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/13.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/14.png)
=(x
1-x
2,y
1-y
2),
∴(x
1-x
2)
2+(y
1-y
2)
2=4.
∴x
12-2x
1x
2+x
22+y
12-2y
1y
2+y
22=4.
∴1-2x
1x
2-2y
1y
2=0.∴2x
1x
2+2y
1y
2=1.
∴(x
1+x
2)
2+(y
1+y
2)
2=1+4+2x
1x
2+2y
1y
2=5+1=6.
∴|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/15.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/16.png)
|=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/17.png)
.
解法二:∵|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/18.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/19.png)
|
2+|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/20.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/21.png)
|
2=2(|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/22.png)
|
2+|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/23.png)
|
2),
∴|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/24.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/25.png)
|
2=2(|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/26.png)
|
2+|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/27.png)
|
2)-|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/28.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/29.png)
|
2=2(1+4)-2
2=6.
∴|
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/30.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/31.png)
|=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/32.png)
.
故選D
點評:求
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/33.png)
常用的方法有:①若已知
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/34.png)
,則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/35.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/36.png)
;②若已知表示
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/37.png)
的有向線段
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/38.png)
的兩端點A、B坐標(biāo),則
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/39.png)
=|AB|=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/40.png)
③構(gòu)造關(guān)于
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/41.png)
的方程,解方程求
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023213537250019583/SYS201310232135372500195004_DA/42.png)
.