名校
1 . 如图,在等腰直角三角形
中,
,
,
,
,
分别是
,
上的点,且
,
,
分别为
,
的中点,现将
沿
折起,得到四棱锥
,连结
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/7ccb2171-6181-490b-99b5-54a849a2f1c3.png?resizew=343)
(1)证明:
平面
;
(2)在翻折的过程中,当
时,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ee826937d2add7a93aaa1422f8b736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.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/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/7ccb2171-6181-490b-99b5-54a849a2f1c3.png?resizew=343)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在翻折的过程中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-07-15更新
|
701次组卷
|
4卷引用:湖北省武汉市华中科技大学附属中学2022-2023学年高二上学期9月月考数学试题
湖北省武汉市华中科技大学附属中学2022-2023学年高二上学期9月月考数学试题湖北省武汉市华中师范大学第一附属中学2023-2024学年高二上学期九月月考数学试题福建省厦门双十中学漳州校区2024届高三上学期10月月考数学试题(已下线)专题06 用空间向量研究距离、夹角问题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)
名校
解题方法
2 . 如图,在三棱柱
中,侧棱![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
底面
,
,
,
,
是
中点,
是
中点,
是
与
的交点,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/75d1aae6-e961-4ed3-bcf0-a553dc632fde.png?resizew=152)
(1)求证:
平面
;
(2)若二面角
的余弦值是
,求点
到平面
的距离.
![](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/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee16c91119c5601a7c93a6642c95e7f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/75d1aae6-e961-4ed3-bcf0-a553dc632fde.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c203fa3cafdc1d924b61ee1d83a3ecf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4e7552a39c412d882766dbcd7eeb69.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa2fb03002a3c4e58c4bf3c81a22c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4e7552a39c412d882766dbcd7eeb69.png)
您最近一年使用:0次
名校
解题方法
3 . 已知直四棱柱
中,底面ABCD为菱形,E为线段
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/cdcb8e55-a683-4770-9c0d-b737c88641e9.png?resizew=167)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
平面
;
(2)若
,则当点E在何处时,CE与
所成角的正弦值为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/cdcb8e55-a683-4770-9c0d-b737c88641e9.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8923f867767455ab4ca0913daa888ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8f6ab40dbad20c5b2527d0d4e11ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4e6eb3663870ed202cc208eaf239dc.png)
您最近一年使用:0次
2022-12-27更新
|
787次组卷
|
2卷引用:云南省曲靖市第一中学2023届高三上学期12月月考数学(理)试题
名校
4 . 如图,长方体
中,
、
分别是
、
的中点,
、
分别是
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/25/41c637c3-4694-4416-8897-75416cc58dae.png?resizew=194)
(1)求二面角
的大小;
(2)求证:
平面
;
(3)求点
到平面PNE的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9722f9f802155f901b0dfd50e73d345f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4217f4375caaeef4d4221143d5f6bbf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/25/41c637c3-4694-4416-8897-75416cc58dae.png?resizew=194)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502f49e759b623b5c3a8b901bb9882cc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
解题方法
5 . 如图,在三棱锥
中,平面
平面
,E,F,N分别为
的中点,点G在
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/b71972f5-7ac5-490c-89a7-d564840874d9.png?resizew=165)
(1)证明:
平面
.
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4744a1e870d49d26222f945fbb4be46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a903ca646c4e9ca53f76a6e3ab62b72.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/b71972f5-7ac5-490c-89a7-d564840874d9.png?resizew=165)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60d66204e1abc17bd01749f187f8050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecf35bb2453db07d66391f501fa7a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2022-12-19更新
|
325次组卷
|
3卷引用:河南金太阳联考创新联盟2022-2023学年高二上学期11月第三次联考数学试题
河南金太阳联考创新联盟2022-2023学年高二上学期11月第三次联考数学试题河南省驻马店市2022-2023学年高二上学期第三次联考数学试题(已下线)江苏省八市2023届高三二模数学试题变式题17-22
名校
6 . 如图,直三棱柱ABC-A1B1C1中,M为BC的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c74b04d7-99c5-488c-b277-c1bc070dc8a9.png?resizew=155)
(1)证明:A1B∥平面AMC1;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffa995ac1b73394a4cecf085527f5e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c74b04d7-99c5-488c-b277-c1bc070dc8a9.png?resizew=155)
(1)证明:A1B∥平面AMC1;
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
您最近一年使用:0次
2022-12-13更新
|
581次组卷
|
2卷引用:黑龙江省哈尔滨市第四中学校2022-2023学年高二上学期第一次月考数学试题
7 . 如图,三棱柱
中侧棱与底面垂直,且
,AB⊥AC,M,N,P分别为
,BC,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f3af5590-c08d-40c4-92e7-a33fcfaa25fd.png?resizew=149)
(1)求证:PN∥面
;
(2)求平面PMN与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc916a3eb3cabc632e7c894320d5e412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f3af5590-c08d-40c4-92e7-a33fcfaa25fd.png?resizew=149)
(1)求证:PN∥面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求平面PMN与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,底面ABCD是平行四边形,E,F分别是CD,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/a7594f3f-1235-449f-abc9-c2ebee1a4fcc.png?resizew=140)
(1)证明:
平面PAD.
(2)若四棱锥
的体积为32,
的面积为4,求B到平面DEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/a7594f3f-1235-449f-abc9-c2ebee1a4fcc.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
您最近一年使用:0次
2022-12-03更新
|
836次组卷
|
5卷引用:江西省九江第一中学2023届高三上学期12月月考数学(文科)试题
名校
解题方法
9 . 如图所示的几何体是由等高的
个圆柱和半个圆柱组合而成,点G为
的中点,D为
圆柱上底面的圆心,DE为半个圆柱上底面的直径,O,H分别为DE,AB的中点,点A,D,E,G四点共面,AB,EF为母线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/8af8d836-1e50-43b9-bcdb-f1e5b4fda145.png?resizew=172)
(1)证明:
平面BDF;
(2)若平面BDF与平面CFG所成的较小的二面角的余弦值为
,求直线OH与平面CFG所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c44512cb86bcf48c6d21357f45b533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/8af8d836-1e50-43b9-bcdb-f1e5b4fda145.png?resizew=172)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97776c09f988638731deef0bad52cb46.png)
(2)若平面BDF与平面CFG所成的较小的二面角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
您最近一年使用:0次
2022-11-26更新
|
480次组卷
|
5卷引用:河南省商丘市部分学校2022-2023学年高三上学期11月质量检测理科数学试题
名校
10 . 如图,在四棱锥
中,
,AB⊥BC,CD=2AB,PA⊥平面ABCD,E为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/c9d927e1-c1b5-4752-b8aa-d547dd1118e6.png?resizew=152)
(1)证明:
平面PBC;
(2)若PA=CD=2BC,求AE与面PBD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/c9d927e1-c1b5-4752-b8aa-d547dd1118e6.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc521258fcaeaf7acffc5ae98c3af6d9.png)
(2)若PA=CD=2BC,求AE与面PBD所成角的正弦值.
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2022-11-19更新
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632次组卷
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2卷引用:黑龙江省哈尔滨师范大学附属中学2022-2023学年高三上学期11月月考数学试题