解题方法
1 . 如图,在长方体
中,
为
的中点,
分别是直线
上的动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/6d7404b5-9864-4670-91d7-01c704fa17da.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25d9b4caaaa4713f730eaec17a4929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d13ee1e498c7a7c3acac81075de3df2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/6d7404b5-9864-4670-91d7-01c704fa17da.png?resizew=163)
A.三棱锥![]() |
B.![]() |
C.直线![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
2 . 在①
,②
,③
,这三个条件中选择一个,补充在下面问题中,并给出解答.
如图,在五面体
中,已知___________,
,
,且
,
.
(1)求证:平面
平面
;
(2)求直线
与平面
夹角的余弦值;
(3)线段
上是否存在一点
,使得平面
与平面
夹角的余弦值等于
,若存在,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57cb0d726cc25a350dc792b539ff2f2.png)
如图,在五面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc22c901160e072ae13a66f62c489f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05426a41ec7b22c0445bfe78d786c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7422660f0635be92e11838af5f4b4b5e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/a71615f2-2014-4d94-8188-c5de6a950aa6.png?resizew=148)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293a2e244834864e78e93d8c13be6905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72acf5ee54c89dede4358c61ecd7a101.png)
您最近一年使用:0次
3 . 如图,在四棱锥
中,
平面
,
,
,且
,
,
.
(1)求证:
;
(2)在线段
上,是否存在一点M,使得平面
与平面
所成角的大小为
,如果存在,求
的值,如果不存在,请说明理由.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2478a116f8ff83c8477094e97c4211cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/273d95a5-49f3-478c-b615-7a060d2c389d.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8010e1a73f05117a278860c1c0c7f147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47548785e478bc5b9591341a881e3127.png)
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2023-09-26更新
|
831次组卷
|
3卷引用:宁夏银川市景博中学2023-2024学年高二上学期9月质量检测数学试题
宁夏银川市景博中学2023-2024学年高二上学期9月质量检测数学试题重庆市巫溪县尖山中学校2023-2024学年高二上学期第一次月考数学试题(已下线)第1章 空间向量与立体几何单元测试能力卷-2023-2024学年高二上学期数学人教A版(2019)选择性必修第一册
名校
解题方法
4 . 在边长为2的正方体
中,M,N分别是BC,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.AM与![]() |
B.![]() |
C.点![]() ![]() |
D.若点Q为线段![]() ![]() ![]() |
您最近一年使用:0次
2023-09-05更新
|
706次组卷
|
4卷引用:宁夏回族自治区银川市第二中学2023-2024学年高二上学期第一次月考数学试题
5 . 在正三棱柱中,
,则( )
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
2023-08-03更新
|
738次组卷
|
6卷引用:宁夏回族自治区银川市贺兰县第二高级中学2023-2024学年高二上学期10月第一次阶段性考试数学试题
宁夏回族自治区银川市贺兰县第二高级中学2023-2024学年高二上学期10月第一次阶段性考试数学试题人教A版(2019) 选修第一册 数学奇书 第一章 学业评价(十)人教A版(2019) 选修第一册 数学奇书 第一章 空间向量与立体几何 1.4.2 用空间向量研究距离、夹角问题 第2课时 用空间向量研究夹角问题(已下线)人教A版2019选择性必修第一册综合测试(基础)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)四川省泸州市天立学校2023-2024学年高二上学期10月月考数学试题(已下线)专题05 直线与平面的夹角4种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
名校
解题方法
6 . 如图,在棱长为
的正方体
中,点
,
分别在线段
和
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/cc682383-3e95-4069-b50d-6e36d0bc4277.png?resizew=155)
给出下列四个结论:
①
的最小值为
;
②四面体
的体积为
;
③有且仅有一条直线
与
垂直;
④存在点
,
,使
为等边三角形.
其中所有正确结论的序号是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/cc682383-3e95-4069-b50d-6e36d0bc4277.png?resizew=155)
给出下列四个结论:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
②四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb1d7bd70e898d08f78de751294df1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
③有且仅有一条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
④存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbec471ffed534e60ec40d48b9f0968.png)
其中所有正确结论的序号是
您最近一年使用:0次
2023-03-27更新
|
1917次组卷
|
9卷引用:宁夏银川一中2022-2023学年高二下学期期中考试数学(理)试题
宁夏银川一中2022-2023学年高二下学期期中考试数学(理)试题(已下线)专题02 空间向量与空间角、空间距离【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)(已下线)高二上期中真题精选(易错60题30个考点专练)【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)北京市西城区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题08空间向量与立体几何北京卷专题19B空间向量与立体几何(选择填空题)北京市昌平区第一中学2024届高三上学期期中考试数学试题北京市陈经纶中学2023-2024学年高三上学期数学阶段性诊断练习6
名校
7 . 已知正四棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/c81d9174-ed0b-4a83-8353-377d84df0293.png?resizew=147)
(1)求证:
;
(2)求二面角
的余弦值;
(3)在线段
上是否存在点
,使得平面
平面
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/c81d9174-ed0b-4a83-8353-377d84df0293.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dea8dd46bcd7473ad04381b4e6d9d3.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc492b4bf027e8eeba9c08ecebb50f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa70b6554a9c50365435afc5742193c.png)
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2021-06-22更新
|
2307次组卷
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7卷引用:2015-2016学年宁夏银川市育才中学高二上学期期末理科数学试卷
2015-2016学年宁夏银川市育才中学高二上学期期末理科数学试卷重庆市荣昌中学校2020-2021学年高二上学期十月月考数学试题湖北省武汉市洪山高级中学2021-2022学年高二上学期第一次月考数学试题(已下线)1.4 空间向量的应用(精练)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)黑龙江省大庆实验中学2021届高三得分训练(二)数学(理)试题(已下线)专题04 二面角(含探索性问题)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)(已下线)专题18 立体几何综合-备战2022年高考数学(理)母题题源解密(全国乙卷)
名校
8 . 如图,
平面
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2019/7/16/2247931161116672/2247957236981760/STEM/1791813d9e1b427c94cd33e68c37cc82.png?resizew=235)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc77e828650bc522b229a9d11e0197c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f01fb34062af96f8ba7e1e05fb5f862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24914bb2ddc7a5d0cb8772ea5fd31401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4568a33b56a5683c5bd4ff3a05fb32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e61dcea246d9be228d26796f59443bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2019/7/16/2247931161116672/2247957236981760/STEM/1791813d9e1b427c94cd33e68c37cc82.png?resizew=235)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69c2344dc6a9f77a169f2b320263418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fa442c18f1129caf84cb6ff4425fe4.png)
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2018-10-21更新
|
1137次组卷
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3卷引用:宁夏石嘴山市第三中学2019-2020学年高二上学期期末考试数学(理)试题
2014·广东湛江·一模
名校
解题方法
9 . 在如图所示的几何体中,四边形
为平行四边形,
,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571681095139328/1571681100988416/STEM/d2fd3c26c0c84c68ab2b1ec536cbb2ac.png?resizew=217)
(1)若
是线段
的中点,求证:
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c30de91ed42df92510cb64548fe704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05f315ab14567942f699983b60d04be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6034301fc4110da89bdb0f46ad82ab.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571681095139328/1571681100988416/STEM/d2fd3c26c0c84c68ab2b1ec536cbb2ac.png?resizew=217)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895bdd0286b8e2704fee9c343d82f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9cd88984f891a49ab451a06410a1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b820c84570da9c38d0a81c22788b76.png)
您最近一年使用:0次
2016-12-02更新
|
1477次组卷
|
3卷引用:宁夏银川唐徕回民中学2019-2020学年高二12月数学(理)试题
宁夏银川唐徕回民中学2019-2020学年高二12月数学(理)试题甘肃省金昌市永昌县第一高级中学2020-2021学年高二上学期期末数学(理)试题(已下线)2014届广东省湛江市高三高考模拟测试二理科数学试卷