题目
题型:不详难度:来源:
如图,正方形ADEF和等腰梯形ABCD垂直,已知BC=2AD=4,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015907-16182.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015907-46597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015907-93675.gif)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015907-53312.gif)
(II)求异面直线BE与AC所成的角的余弦值;
(III)在线段BE上是否存在一点P,使得平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-10301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-33464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-86521.jpg)
答案
(1)略
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-51817.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-51817.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-38726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-57013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-19869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-63394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-23812.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015910-24935.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-38726.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-63394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015909-19869.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015910-28005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015910-76710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015910-65229.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015911-88715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015911-93612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015911-88533.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015911-47660.gif)
故可以以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015912-36336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015912-72727.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015912-41381.gif)
……………………………………6分
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015912-84200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015912-10769.gif)
即异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-54218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-21934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-37040.gif)
⑶解:若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-43397.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-54218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015914-11780.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-43397.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015914-43222.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015914-79994.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015914-95455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-86535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-80296.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-28920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-73056.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-32114.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015916-57646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015914-95455.gif)
同理可求得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015916-30070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-86535.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015916-41983.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015916-21040.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015916-43882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015915-86535.gif)
故存在这样的点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015913-43397.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015908-51817.gif)
核心考点
试题【(本小题满分12分)如图,正方形ADEF和等腰梯形ABCD垂直,已知BC=2AD=4,,(I)求证:面ABF;(II)求异面直线BE与AC所成的角的余弦值;(I】;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/20191021/20191021015859-74191.png)
①平面EFG//平面PBC
②平面EFG
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015900-49087.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015900-11921.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015900-26034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015900-63991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015852-44577.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015852-37403.gif)
(Ⅰ)确定点G的位置;
(Ⅱ)求三棱锥C1—EFG的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015852-61232.jpg)
在三棱锥ABCD中,平面DBC⊥平面ABC,△ABC为正三角形, AC=2,DC=DB=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015846-84001.gif)
(1)求DC与AB所成角的余弦值;
(2)在平面ABD上求一点P,使得CP⊥平面AB D.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015846-39681.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015840-77741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-69319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-55928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-69319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-52773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-44117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015841-69319.png)
A.直线 | B.圆 | C.抛物线 | D.双曲线 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015842-61112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015831-81219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015831-73199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015832-49116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015832-20765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015832-65055.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015832-85154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015832-38203.gif)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-37588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-24336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-37588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-92439.gif)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-37746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015833-92439.gif)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015834-57985.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021015834-35144.gif)
最新试题
- 1某物体运动的速度图象如图所示,已知物体质量为1kg,根据图象可知[ ]A.前2s内物体的位移为6m B.前2s内
- 2人站在平面镜前2 m处,他在镜中的像距平面镜为 m。若人以 0.5 m/s速度垂直向平
- 3在“探究滑动摩擦力的大小与什么因素有关”的实验中,同学们提出了如下猜想:A.滑动摩擦力大小可能与压力大小有关B.滑动摩擦
- 4某市寻找适合布局工厂的地点,该厂址要满足两个条件:①地形平坦;②距河流1km范围内。下图中“空问资料”是该市地形与河流的
- 5弹簧秤下挂一个物体,弹簧秤的示数为a,如果把物体浸没在水中,读出弹簧秤的示数为a/4,那么这个物体的密度是( )A.0
- 6阅读下文,回答问题。论语(节选) 子曰:“学而时习之,不亦说乎?有朋自远方来,不亦乐乎?人不知而不愠,不亦君子乎?”
- 7设z1=1-i,z2=a+2ai(a∈R),其中i 是虚数单位,若复数z1+z2 是纯虚数,则a=______.
- 8阅读短文, 用完整的句子回答问题.The first Earth Day was in 1970.People were
- 9(9分)一小球沿光滑斜面向下运动,用每隔0.1s曝光一次的频闪照相机拍摄下不同时刻小球的位置照片如图所示,选小球的五个连
- 10向醋酸溶液中滴加氢氧化钠溶液,则 ( )A.醋酸的电离平衡向左移动B.溶液的PH减小C.醋酸根离子物质的量
热门考点
- 1“劳模”可以说是无私奉献,艰苦奋斗的代名词。然而,姚明当选为“全国劳模”,使人们对“劳模”和艰苦奋斗精神有了更多的思考。
- 2与台湾省隔海相望的是广东省。[ ]
- 32013年11月3日,北京时间3日19:05开始,本世纪第二次日全环食上演。全球各地天文爱好者用相机拍摄了这美丽难得的瞬
- 4小于3的正整数是______.
- 5“神农因天之时,分地之利,制耒耜,教民农耕。”材料中的“神农”是A.炎帝B.黄帝C.尧D.舜
- 6党的十八届三中全会的《决定》开宗明义地明确“市场在资源配置中起决定性作用”。这种决定作用是通过 ( )A.价
- 7现有已调节好的弹簧测力计、橡皮泥、细线、装有足量水的烧杯.小明同学设计一个实验.验证浸没在水中的物体所受的浮力是否与物体
- 8某工厂用7万元钱购买了一台新机器,运输安装费用2千元,每年投保、动力消耗的费用也为2千元,每年的保养、维修、更换易损零件
- 9下列句子中没有语病的一项是( )A.近年来相继发生的“毒奶粉”、“瘦肉精”、“地沟油”、“毒豆芽”等事件足以表明,诚
- 10、粘土胶体溶液中,粘土粒子带负电,为了使粘土粒子聚沉,下列物质中用量最少,最有效的电解质是……( ) A.Na3PO4B