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已知:四棱锥P-ABCD的底面ABCD是边长为1的正方形,PD⊥底面ABCD,且PD=1.
(Ⅰ)求证:BC∥平面PAD;
(Ⅱ)若E、F分别为PB、AD的中点,求证:EF⊥平面PBC;
(Ⅲ)求二面角B-PA-C的余弦值.
考点分析:
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一个袋子里装有大小相同,且标有数字1~5的若干个小球,其中标有数字1的小球有1个,标有数字2的小球有2个,…,标有数字5的小球有5个.
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△ABC中,角A、B、C的对边分别为a,b,c.
(Ⅰ)若
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,求cosA的值;
(Ⅱ)若A∈[
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746014_ST/1.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746014_ST/2.png)
],求
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的取值范围.
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在△ABC中,E、F分别为AB、AC上的点,若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746013_ST/0.png)
=m,
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=n,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746013_ST/2.png)
=mn.拓展到空间:在三棱锥S-ABC中,D、E、F分别是侧棱SA、SB、SC上的点,若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746013_ST/3.png)
=m,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746013_ST/4.png)
=n,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746013_ST/5.png)
=p,则
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=
.
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设常数a>0,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746012_ST/0.png)
展开式中x
3的系数为-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746012_ST/1.png)
,则a=
,
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=
.
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已知曲线C的参数方程是:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746011_ST/0.png)
(θ为参数),则曲线C的普通方程是
;曲线C被直线x-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023214036230874661/SYS201310232140362308746011_ST/1.png)
y=0所截得的弦长是
.
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