1 . 如图,在长方体
中,底面
是边长为2的正方形,
,E,F分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6cab89c2-fd72-44c1-a5e0-d64293b834c0.png?resizew=156)
(1)求证:
∥平面
;
(2)设H在棱
上,且
,N为
的中点,求证:
平面
;并求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4893fbcb191420e06a239e63493626f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cab95678b6f65bc7d15f8f609352c9c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6cab89c2-fd72-44c1-a5e0-d64293b834c0.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850e88507969a07a9515347b97c7b6e.png)
(2)设H在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34648df9ac785a84ec3f01b005aed5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247157c37eb7c3ae9ac5aa7efb69c3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850e88507969a07a9515347b97c7b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850e88507969a07a9515347b97c7b6e.png)
您最近一年使用:0次
2022-05-17更新
|
888次组卷
|
3卷引用:北京市朝阳区2022届高三二模数学试题
名校
2 . 在如图所示的几何体中,四边形
是正方形,四边形
是梯形,
,
,平面
平面
,且
.
平面
;
(2)求平面
与平面
所成角的大小;
(3)已知点
在棱
上,且异面直线
与
所成角的余弦值为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bce6eba5d07a34f24c5370c580ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2638327a2b0d6219141d54a0fe7f94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3025e649f4d4bc6bbda122f940cf8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c032261d2f887de100ed40e8fc676e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ea2d880b20542c2d813f95c683403e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2bcbaa7dadd999705543ab63581e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955e030d649a3c7885071b4bf849993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1956db288a5a3b8c97d2539e9e5e4f85.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7246b49f9c9b524db7a8929133cb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b7679d26c1041b17e43100775ebc2a.png)
您最近一年使用:0次
2022-04-19更新
|
1195次组卷
|
6卷引用:北京市朝阳区北京工业大学附属中学2022-2023学年高二上学期10月月考数学试题
北京市朝阳区北京工业大学附属中学2022-2023学年高二上学期10月月考数学试题天津市新华中学2022届高三下学期4月统练数学试题天津市静海区第一中学2022届高三下学期5月考前学业能力调研数学试题天津市滨海新区塘沽第一中学2023届高三下学期十二校联考(二)数学模拟试题(已下线)专题1.11 空间角的向量求法大题专项训练(30道)-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)天津市滨海新区实验中学滨海学校2024届高三上学期期中质量调查数学试题
名校
3 . 如图,在正三棱柱
中,D为棱
上的点,E,F,G分别为
,
,
的中点,
.
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943024912302080/2943173408899072/STEM/5d9d6b1e3df74e6882ec0fc8fa23ec86.png?resizew=290)
(1)求证:
;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
平面
,试确定D点的位置,并求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943024912302080/2943173408899072/STEM/5d9d6b1e3df74e6882ec0fc8fa23ec86.png?resizew=290)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ce1335e489c2b0835d7e16ea765e1e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
您最近一年使用:0次
2022-03-24更新
|
553次组卷
|
2卷引用:北京市人大附中2022届高三3月数学统练(二)试题
名校
解题方法
4 . 如图,
矩形
所在的平面,
分别是
的中点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc3ccd144e442740fe9fa99b3f823cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/f4ef6038-f85a-4702-be98-baf10391a7c3.png?resizew=196)
(1)求证:
;
(2)平面
和平面
所成角的余弦值;
(3)在线段
上是否存在一点
,使
平面
?若不存在,说明理由;若存在,确定点
的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc3ccd144e442740fe9fa99b3f823cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/f4ef6038-f85a-4702-be98-baf10391a7c3.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab384f2520d76ed8fa01b31e09c1eea.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe796b7c22effa662311e919676faeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2022-01-03更新
|
982次组卷
|
3卷引用:北京市朝阳区2022-2023学年高二上学期11月期中考试数学试题
名校
5 . 如图,在四棱锥
中,底面
是边长为4的正方形,
是等边三角形,
平面
,E,F,G,O分别是PC,PD,BC,AD的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965614666448896/2967107647184896/STEM/6fbd1ff5-37dc-414d-9e3d-7c14c9345937.png?resizew=221)
(1)求证:
平面
;
(2)求平面
与平面
的夹角的大小;
(3)线段PA上是否存在点M,使得直线GM与平面
所成角为
,若存在,求线段PM的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965614666448896/2967107647184896/STEM/6fbd1ff5-37dc-414d-9e3d-7c14c9345937.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)线段PA上是否存在点M,使得直线GM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
您最近一年使用:0次
2022-04-27更新
|
2372次组卷
|
33卷引用:北京市朝阳区清华大学附属中学朝阳学校2021-2022学年高二上学期期中数学试题
北京市朝阳区清华大学附属中学朝阳学校2021-2022学年高二上学期期中数学试题2020届山东省潍坊市高三2月数学模拟试题(一)(已下线)备战2020年高考数学之考场再现(山东专版)062020届山东省寿光市第二中学高三线上2月29日数学高考模拟题(三)2020届北京八中高三3月学模拟考试数学(二)试题2020届北京市第八中学高三下学期自主测试(二)数学试题山东省日照五莲县丶潍坊安丘市、潍坊诸城市、临沂兰山区2020届高三6月模拟数学试题天津市北辰区2020届高考二模数学试题(已下线)第9篇——立体几何与空间向量-新高考山东专题汇编(已下线)专题16 立体几何-2020年高考数学母题题源解密(北京专版)天津市南开中学2020-2021学年高二上学期期中数学试题北京市第十二中学2020-2021学年高二12月月考数学试题天津市河西区2021-2022学年高二上学期期中数学试题北京交通大学附属中学2021-2022学年高二上学期期末考试数学试题(已下线)第3讲 立体几何中的向量方法(讲)-2022年高考数学二轮复习讲练测(新教材地区专用)(已下线)类型三 立体几何与空间向量-【题型突破】备战2022年高考数学二轮基础题型+重难题型突破(新高考专用)天津市部分区2022届高三下学期质量调查(一)数学试题天津市南开区2022届高三下学期三模数学试题甘肃省张掖市临泽县第一中学2021-2022学年高二下学期期中考试数学(理)试题天津市和平区第二十中学2022-2023学年高三上学期期中数学试题广西桂林市中山中学2022-2023学年高三上学期10月月考数学试题北京市石景山区2019-2020学年高三上学期期末考试数学试题天津市滨海新区2023届高三三模数学试题黑龙江省牡丹江市第二高级中学2023届高三上学期期中数学试题(已下线)高二上学期期中【全真模拟卷02】(人教A版2019)(原卷版)江苏省郑梁梅高级中学2022-2023学年高二下学期4月月考数学试题天津市九十六中学2022-2023学年高二上学期期末数学试题天津市蓟州区第一中学2023-2024学年高三上学期第一次学情调研数学试题江西省贵溪市实验中学2024届高三上学期新高考模拟检测(三)数学试题吉林省长春市第六中学2023-2024学年高二上学期1月期末考试数学试题天津市北师大静海实验学校2023-2024学年高二上学期第三次月考数学试题四川省眉山市北外附属东坡外国语学校2023-2024学年高二下学期开学考试数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点1 平面法向量求法及其应用(一)【培优版】
6 . 刍甍(chú méng)是中国古代数学书中提到的一种几何体.《九章算术》中有记载“下有袤有广,而上有袤无广”,可翻译为:“底面有长有宽为矩形,顶部只有长没有宽为一条棱.”如图,在刍甍
中,四边形
是正方形,平面
和平面
交于
.
![](https://img.xkw.com/dksih/QBM/2022/2/27/2913341073735680/2925903899746304/STEM/fe85615f-911c-442b-9074-ae46dcc43593.png?resizew=176)
(1)求证:
平面
;
(2)若
,
,
,
,再从条件①,条件②,条件③中选择一个作为已知,使得刍甍
存在,并求平面
和平面
夹角的余弦值.
条件①:
,
;
条件②:平面
平面
;
条件③:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2022/2/27/2913341073735680/2925903899746304/STEM/fe85615f-911c-442b-9074-ae46dcc43593.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe43b94a84f969479064474603599797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeedb5f361a1baff6338436fff6c471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869dbfaf24d441c4ce3a2b8db86cd2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678988261e6fd7c4f1199c0204a8045d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8baaea02eaa7e473fb2a8f84ba575c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40e867f1d3377cf4fb9ae730d04cf7.png)
条件②:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c1acdd27cebb11e0266464b03b3afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件③:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2af539ca4fdc2fa94d4986537b6598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-02-28更新
|
539次组卷
|
4卷引用:北京市朝阳区2022届高三上学期期末统一检测数学试题
7 . 如图1,在四边形
中,
,
,
,
,
,
分别是
,
上的点,
,
,
,
.将
沿
折起到
的位置,得到五棱锥
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/461e368e-79ac-41cd-b6b8-f20d3be6cc65.png?resizew=430)
(1)求证:
平面
;
(2)若平面
平面
,
(i)求二面角
的余弦值;
(ii)对线段
上任意一点
,求证:直线
与平面
相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b57e28b1d9eebfe35df29d9f61bfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85bdcc2742be52cc80ba7dbe79f9a574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64d857c9e44dc69b19e1587e2aa677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e895a97e8a0332e74195d08ba9ab7780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cfeb35addf27f2379a8e5f87c9b952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f316be3cc6b7c9f725888f714c0b8b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2d555062f34d5a74f6d47da4ea8888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ecdb6170c4f750ffa6e44b43d0dbd2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/461e368e-79ac-41cd-b6b8-f20d3be6cc65.png?resizew=430)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd305d8340a61937bf44afa9a75329f.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004dd8ad9e5a200b3869ebfc59c2446d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a247c4f11824d034046f88fc79b069f5.png)
(i)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a89e2d48c57d56f20917c10a5b7b2d0.png)
(ii)对线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
您最近一年使用:0次
解题方法
8 . 在四棱锥
中,
平面
,底面四边形
为直角梯形,
,Q为
中点.
![](https://img.xkw.com/dksih/QBM/2021/9/29/2818649303842816/2819158951124992/STEM/29de6c722c6d40e0b5b7d814268ce4b5.png?resizew=199)
(Ⅰ)求证:
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffce1ae307efa0ecd4af0e9a8a9537c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/9/29/2818649303842816/2819158951124992/STEM/29de6c722c6d40e0b5b7d814268ce4b5.png?resizew=199)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ec6a1e64b7eb52b70f3dce9fc043cc.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2021-09-30更新
|
339次组卷
|
3卷引用:北京朝阳和平街一中2020-2021学年高二上学期期中数学试题
名校
解题方法
9 . 如图,四棱柱
的侧棱
平面ABCD,四边形ABCD为菱形,E,F分别为
,
的中点.
,
.
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834327540457472/2834918643916800/STEM/ced98b83-e7b0-435a-926b-53b9145a62ea.png?resizew=252)
(1)证明:B,E,
,F四点共面;
(2)求直线AE与平面
所成角的正弦值;
(3)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://img.xkw.com/dksih/QBM/2021/10/21/2834327540457472/2834918643916800/STEM/ced98b83-e7b0-435a-926b-53b9145a62ea.png?resizew=252)
(1)证明:B,E,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
(2)求直线AE与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在三棱柱
中,四边形
是边长为
的正方形,
.再从条件①、条件②、条件③中选择两个能解决下面问题的条件作为已知,并作答.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/b6074e51-f458-446e-9c39-12eba4c614c9.png?resizew=169)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
条件①:
;条件②:
;条件③:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/b6074e51-f458-446e-9c39-12eba4c614c9.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d399572bdc5816897500121034d1100c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
您最近一年使用:0次
2021-05-07更新
|
1260次组卷
|
7卷引用:北京市朝阳区2021届高三下学期二模数学试题