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如图,l1、l2、l3是同一平面内的三条平行直线,l1与l2间的距离是1,l2与...
如图,l
1、l
2、l
3是同一平面内的三条平行直线,l
1与l
2间的距离是1,l
2与l
3间的距离是2,正三角形ABC的三顶点分别在l
1、l
2、l
3上,则△ABC的边长是( )
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289002_ST/images0.png)
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289002_ST/0.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289002_ST/1.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289002_ST/2.png)
D.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289002_ST/3.png)
考点分析:
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已知点P的极坐标是(1,π),则过点P且垂直极轴所在直线的直线方程是( )
A.ρ=1
B.ρ=cosθ
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289001_ST/0.png)
D.
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289000_ST/images0.png)
如图,PA为⊙O的切线,A为切点,PO交⊙O于点B,PA=8,OA=6,则tan∠APO的值为( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289000_ST/0.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289000_ST/1.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429528959/SYS201310251237434295289000_ST/2.png)
D.
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点O是梯形ABCD对角线的交点,|AD|=4,|BC|=6,|AB|=2.设与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/0.png)
同向的单位向量为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/1.png)
,与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/2.png)
同向的单位向量为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/3.png)
.
(1)用
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/4.png)
和
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/5.png)
表示
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/6.png)
和
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/7.png)
;
(2)若点P在梯形ABCD所在平面上运动,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/8.png)
,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272011_ST/9.png)
的最大值和最小值.
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如图所示,在△ABC中,D、F分别是BC、AC的中点,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/0.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/1.png)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/2.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/3.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/4.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/5.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/6.png)
.
(1)用
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/7.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/8.png)
表示向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/9.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/10.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/11.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/12.png)
、
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272010_ST/13.png)
;
(2)求证:B、E、F三点共线.
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设i、j分别是平面直角坐示系Ox,Oy正方向上的单位向量,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272009_ST/0.png)
=-2i+mj,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272009_ST/1.png)
=ni+j,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123743429527294/SYS201310251237434295272009_ST/2.png)
=5i-j,若点A、B、C在同一条直线上,且m=2n,求实数m、n的值.
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