题目
题型:不详难度:来源:
四棱锥P-ABCD中,底面ABCD为直角梯形,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-43682.png)
PA⊥底面ABCD,PD与底面ABCD成
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-86540.png)
(1)点H在AC上且EH⊥AC,求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-44543.png)
(2)求AE与平面PCD所成角的余弦值;
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-18661.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-74102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-39215.png)
解析
则由条件知,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-51826.png)
而:PA⊥底面ABCD,PD与底面ABCD成
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-86540.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-43220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-98966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-69670.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-99225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-70624.png)
由EH⊥AC得,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-45674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-69095.png)
第二问由上得,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-42335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-37397.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-81781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-48507.png)
记平面PCD的一个法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-66134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-85719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-22237.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-70910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034752-90981.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034752-70334.png)
解(1) 以AB,AD,AP分别为x,y,z轴,建立如图所示的坐标系。
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034752-94772.png)
则由条件知,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-51826.png)
而:PA⊥底面ABCD,PD与底面ABCD成
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-86540.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-43220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-98966.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034748-69670.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-99225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-70624.png)
由EH⊥AC得,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-45674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034749-69095.png)
∴所求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034747-74102.png)
(2)由上得,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-42335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-37397.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-81781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034750-48507.png)
记平面PCD的一个法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-66134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-85719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-22237.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034751-70910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034752-90981.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034752-70334.png)
设AE与平面PCD所成角为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034753-79592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034753-87876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034753-68146.png)
核心考点
试题【本题满分14分)四棱锥P-ABCD中,底面ABCD为直角梯形,,AD∥BC, AB="BC=2," AD="4," PA⊥底面ABCD,PD与底面ABCD成角,】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034740-67843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034741-47783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034741-53914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034741-45337.png)
A.![]() | B.![]() ![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() |
如图:梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034729-82980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-27874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-56868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-17146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-95789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-57315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-80693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-80818.png)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-79272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034730-61237.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034731-75391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034731-97352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034715-43217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034716-40028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034716-19478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034716-16721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034716-24321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034717-24709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034717-62089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034717-40509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034718-19305.png)
在如图所示的几何体中,四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-54431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-70082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-54431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-70467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-60785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-71353.png)
(Ⅰ)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-37422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-56242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-56436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034700-13573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034701-45684.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034701-16728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034701-80532.png)
(Ⅲ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034701-20311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034649-96236.png)
PD=1,PC=
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034649-69535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034649-64835.jpg)
(Ⅰ)求证:PD⊥面ABCD;
(Ⅱ)求二面角A-PB-D的大小.
最新试题
- 1---No words are strong enough to express our thanks for your
- 2I was packed and ready to leave for my two days’ trip. My mi
- 3下面加横线词语的字音完全正确的一项是 [ ]A.菜畦(w ā) 澎湃(p ài) 嫉(j ì
- 4阅读下列材料(13分)材料一 我们的制度之所以成为民主政治,因为政权是在全体公民手中,而不是在少数人手中。……每个人在法
- 5火箭在大气中飞行时,它的头部跟空气摩擦生热,温度可达几千摄氏度.在火箭头上涂一层特殊材料,这种材料在高温下发生
- 6在某公园建有一山坡滑草运动项目,该山坡可看成倾角θ=37°的斜面,一名游客连同滑草装置总质量m=80kg,他从静止开始从
- 7When you feel _____ to watch TV by then, you are all right.A
- 8下列关于油脂的说法不正确的是( )A.油脂属于酯类B.油脂密度比水小,不溶于水,会浮于水上层C.油脂没有固定的熔沸点D
- 9将等物质的量的SO2气体和Cl2同时作用于湿润的红色布条,则布条的颜色( )A.变白色B.变无色C.不褪色D.先褪色后
- 10秦岭——淮河一线大致同哪些界线相一致( )①1月份00等温线 ②400毫米等降水量线 ③800
热门考点
- 1下表是某地市场销售的一种“加碘食盐”包装袋上的部分文字说明。(1)碘酸钾属于__________(填“氧化物”、“酸”或
- 2用所给单词的适当形式填空。1. After work, he often plays the guitar at hom
- 3.____the meeting should last two days or three days doesn’t
- 4如果某男患病,则可推知其母亲及女儿都有此病,那么该病的致病基因是 [ ]A.X染色体上的显性遗传 B.常染色体上
- 5质量为m的汽车在平直的公路上以初速度v.开始做加速运动,经过时间t前进了x时,速度达到最大值Vm,若汽车在加速的过程中发
- 6烧热水时,水在沸腾后继续加热,水的温度将______(选填“升高”、“降低”或“保持不变”).喝热水时,发现杯子的上半部
- 7阅读下面的文字,完成题目。(12分)荀子主张以礼治国。“礼”从政治上讲,指国家制订的政治法律制度。从伦理上讲,指国家提倡
- 8在下列实验中,不能达到目的的是A.用NaHCO3鉴别低级醇和低级羧酸B.用石墨做电极电解Mg(NO3)2、Cu(NO3)
- 9(1)已知x2=y3=z5,且3x+4z-2y=40,求x,y,z的值;(2)已知:两相似三角形对应高的比为3:10,且
- 10--- You should have recited the text yesterday. --- _______.