题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-69989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-21432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-95658.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-18428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-64514.gif)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-34439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-73566.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-67468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-17391.gif)
答案
依题设知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-57293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-86422.gif)
(Ⅰ)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-36663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-60763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-41461.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-50626.gif)
由三垂线定理知,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-85713.gif)
在平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-23484.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-54660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-41651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-96538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-94463.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-97911.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-10053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-27827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-46442.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-83571.gif)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-31344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-41651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-73566.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-20322.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043923-41651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-21996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-73566.gif)
(Ⅱ)作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-95873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-96392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-81986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-17306.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043924-92051.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-67468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-90415.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-71821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-26491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-63982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-39289.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-33882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-21276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-25712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043925-60546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-67468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-72039.gif)
解法二:
以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-57174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-11172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-57753.gif)
建立如图所示直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-70659.gif)
依题设,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-55833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-89405.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043926-67198.gif)
(Ⅰ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-50296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-87317.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-67252.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-68124.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-33759.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043921-34439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-50823.gif)
(Ⅱ)设向量
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-89468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043927-44081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043928-62820.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043928-85342.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043928-40474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043928-44806.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043928-92649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043929-32526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043929-35222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043929-64470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043929-49017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-67468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043929-89205.gif)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043922-67468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043930-93760.gif)
解析
核心考点
试题【如图,正四棱柱中,,点在上.(1)证明:平面;(2)求二面角的大小.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043910-99936.gif)
形,侧面PAD与底面ABCD垂直,M为底面内的一个动点,且满 足MP=MC,则动点M的轨迹为 ( )
A.椭圆 | B.抛物线 |
C.双曲线 | D.直线 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043857-53287.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043857-62213.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043857-92121.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043858-49675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043858-20412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043858-11579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043858-68805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043858-80452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043859-99406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043859-34551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043859-67757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043859-85838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043859-78031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043900-87714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043849-94777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043850-56319.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043850-89407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043850-23267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043850-38855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043850-23253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043851-36792.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043851-23771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043851-34826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043851-35931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043851-97608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043852-38402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043852-88157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043852-39505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043852-88571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043846-80841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-71360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-39615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-16793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-39755.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-16793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-39755.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043846-80841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-71360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043847-39615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043839-98760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043839-11633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043840-14545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021043840-90854.gif)
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