2024·全国·模拟预测
名校
1 . 如图.在四棱锥
中,已知底面
为矩形,侧面
是正三角形,面
底面
,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/14b8f045-1a15-418a-8853-543a766acd78.png?resizew=178)
(1)证明:
;
(2)若
,且二面角
的大小为
,求异面直线
与
所成角的正切值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/14b8f045-1a15-418a-8853-543a766acd78.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a52818f1e8b7c27f207abae182a64d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
名校
2 . 如图,多面体
中,
平面
,且
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/4d3eec6a-5603-43c8-ad40-45d8fceba45f.png?resizew=123)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5604c1bd07a7806c630a1fba284d5703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147e7c8ba0bbb540a712f6eb2ed6d22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad05c15462132479d1697d5c701027dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fec4e7765094e714baf5e02405cd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91333d97c74d94aba4391a88834185b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/4d3eec6a-5603-43c8-ad40-45d8fceba45f.png?resizew=123)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b766876252d16f2e331ef2893d45cf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b2ef1b525d302da087241e37387fa6.png)
您最近一年使用:0次
2023-10-15更新
|
281次组卷
|
3卷引用:重庆市杨家坪中学2023-2024学年高二上学期第一次月考数学试题
3 . 如图,四棱锥的底面
是边长为
的菱形,
,
,
,平面
平面
,E,F分别为
,
的中点.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2023-11-07更新
|
621次组卷
|
5卷引用:重庆市外国语学校2023-2024学年高二上学期期中数学试题
名校
4 . 如图1,在平面四边形
中,
,
,
,
.将
沿
折起,形成如图2所示的三棱锥
,
.点E,F,G分别为线段
,
,
的中点.
(1)求证:
.
(2)若
,
为线段
上一点(不含端点),求二面角
正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7e75a2397229711c7fb846f2c9ff38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/d642e6ae-53e6-47b3-b5d0-0682a4ae4a65.png?resizew=369)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d1614b23fa6632b914f9a42fdfb8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb590795f82fb51bcfd9820d76152c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd913a336a77ea15782ea7641ad7a52f.png)
您最近一年使用:0次
名校
5 . 如图所示,在直三棱柱
中,侧面
和侧面
都是正方形且互相垂直,
为
的中点,
为
的中点.求证:
(1)
平面
;
(2)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/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/6dce7865-339a-4396-845c-4955267861dd.png?resizew=148)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d020167b334dfda0dce811c519d323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2023-07-03更新
|
731次组卷
|
7卷引用:重庆市铁路中学2023-2024学年高二上学期期中数学试题
重庆市铁路中学2023-2024学年高二上学期期中数学试题4.2 用向量方法研究立体几何中的位置关系 同步练习-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册3.4.2用向量方法研究立体几何中的位置关系 课时作业2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)1.4 空间向量应用(精讲)-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)四川省成都市武侯高级中学2023-2024学年高二上学期期中数学试题(已下线)专题05 用空间向量研究直线、平面的平行、垂直问题10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A版2019选择性必修第一册)(已下线)专题04 空间中的点、直线、平面与空间向量5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,在四棱锥
中,
平面ABCD,四边形ABCD为菱形,
,
,E为CD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/b4b17224-6766-48da-a368-fea64eb222dd.png?resizew=179)
(1)求证:平面
平面PCD;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e2267c84394668eff2e9f5918de4fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/12/b4b17224-6766-48da-a368-fea64eb222dd.png?resizew=179)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a26a7784c7419d8359fb119c8ecc03d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2023-03-11更新
|
515次组卷
|
4卷引用:重庆市杨家坪中学2022-2023学年高二下学期第一次月考数学试题
7 . 如图,在三棱柱
中,
⊥平面
,
是边长为2的正三角形,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/268d39fb-0456-4e5a-ad9d-198fa7ab922e.png?resizew=224)
(1)求证:
⊥平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/268d39fb-0456-4e5a-ad9d-198fa7ab922e.png?resizew=224)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
名校
8 . 如图,在直三棱柱ABC-A1B1C1中,AA1=AB=AC=1,AB⊥AC,M,N,Q分别为CC1,BC,AC的中点,点P在线段A1B1上运动,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/7d32007d-3f04-41ce-86bf-06121356e06a.png?resizew=222)
(1)证明:无论λ取何值,总有AM⊥平面PNQ;
(2)是否存在点P,使得平面PMN与平面ABC的夹角为60°?若存在,试确定点P的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c019910d3e5bec7e0f6f9a6e206a92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/7d32007d-3f04-41ce-86bf-06121356e06a.png?resizew=222)
(1)证明:无论λ取何值,总有AM⊥平面PNQ;
(2)是否存在点P,使得平面PMN与平面ABC的夹角为60°?若存在,试确定点P的位置;若不存在,请说明理由.
您最近一年使用:0次
2022-09-09更新
|
914次组卷
|
8卷引用:重庆实验外国语学校2022-2023学年高二上学期九月检测数学试题
名校
9 . 如图,在三棱柱
中,
平面ABC,D,E,F分别为
,AC,
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/10aa192c-2b71-4d70-a7bf-16c280aa14f1.png?resizew=169)
(1)求证:AC⊥平面BEF;
(2)求点D与平面
的距离;
(3)求二面角
的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa2b0018617bd579875185dafca39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/10aa192c-2b71-4d70-a7bf-16c280aa14f1.png?resizew=169)
(1)求证:AC⊥平面BEF;
(2)求点D与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
您最近一年使用:0次
名校
10 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD是菱形,
,
,E是PB上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/581c5ac5-aba7-4df4-80b6-a2337cdc78dd.png?resizew=230)
(1)求证:
;
(2)已知二面角
的余弦值为
,若E为PB的中点,求EC与平面PAB所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1719410d21e3de1242366ce2965e838c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/581c5ac5-aba7-4df4-80b6-a2337cdc78dd.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5651e38293e0c42a7278af69fa53ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
您最近一年使用:0次
2022-09-29更新
|
1063次组卷
|
12卷引用:重庆市九龙坡区2021-2022学年高二上学期期末数学试题
重庆市九龙坡区2021-2022学年高二上学期期末数学试题2015届湖南省长望浏宁四县高三3月调研(一模)考试理科数学试卷四川省成都市第七中学2016-2017学年高三下学期零诊模拟数学(理)试题四川省成都市第七中学2017-2018学年高二上学期第一次月考数学(理)试题浙江省嘉兴市平湖市2020届高三下学期5月模拟考试数学试题广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题广西2023届高三上学期开学摸底考试数学(理)试题黑龙江省牡丹江市第二高级中学2022-2023学年高三上学期第三次阶段性测试数学试题(已下线)考向28利用空间向量求空间角(重点)广东省揭阳市普宁市华侨中学2023届高三上学期11月期中数学试题江西省南昌市新建区第二中学2024届高三上学期8月开学学业水平检测数学试题广东省河源市龙川县实验中学2024届高三上学期第二次月考数学试题