名校
1 . 如图,在多面体
中,
平面
,
,
为
的中点.
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/a905558f-95df-4f53-b2f6-693787e18ce8.png?resizew=154)
(1)证明:
平面
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff800bc740bbdf43a8893586c601c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7dc43a39738e3e2a0b819be505c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630d82ae0ed6deb825514e0bc92e74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67a9f29dc173b322e3acc4f8ae826d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/a905558f-95df-4f53-b2f6-693787e18ce8.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8f869119803f0c1e091c9ed821cee5.png)
您最近一年使用:0次
2023-04-21更新
|
1144次组卷
|
5卷引用:福建省宁德市福安市福安一中2023-2024学年高三上学期10月月考数学试题
名校
2 . 如图,四棱锥
的底面是梯形,
,
,
,
,平面
平面
,
,
分别为线段
,
的中点,点
是底面
内
包括边界
的一个动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/684f1b4f-3880-49d4-9773-1ed7383f1317.png?resizew=188)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da2ebc3c7d1de745f52ae6908bebf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/684f1b4f-3880-49d4-9773-1ed7383f1317.png?resizew=188)
A.![]() |
B.三棱锥![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-04-13更新
|
1477次组卷
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7卷引用:福建省宁德市霞浦县2022-2023学年高一下学期期中数学试题
福建省宁德市霞浦县2022-2023学年高一下学期期中数学试题黑龙江省齐齐哈尔实验中学等校2022-2023学年高三下学期2月大联考数学试题湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题江苏省镇江第一中学2023-2024学年高三上学期10月月考数学试题(已下线)广东省佛山市南海区桂城中学2024届高三上学期11月月考数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题11-14江苏省2024届高三上学期期末迎考数学试题
名校
3 . 如图,四棱锥P-ABCD的底面ABCD为平行四边形,E为线段AD的中点,
,
,
,BC⊥平面PBE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/00e4784a-6083-4948-a8be-2f0f6281e8e6.png?resizew=220)
(1)证明:PE⊥平面ABCD;
(2)当AD为多少时,平面PBE与平面PCD所成的二面角为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75929268210da5976bc37d080da030dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ed12ab34b0fa225d798a18abc78656.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/00e4784a-6083-4948-a8be-2f0f6281e8e6.png?resizew=220)
(1)证明:PE⊥平面ABCD;
(2)当AD为多少时,平面PBE与平面PCD所成的二面角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
您最近一年使用:0次
2022-11-08更新
|
358次组卷
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2卷引用:福建省宁德市2023届高三上学期期中区域性学业质量检测数学试题(C卷)
解题方法
4 . 如图,在空间四边形
中,
,
,
两两垂直,
,
,
,则点
到直线
的距离为( )
![](https://img.xkw.com/dksih/QBM/2022/7/4/3015287038050304/3015557445787648/STEM/909052f3d060426bbb48fafc4d55a2da.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3b3d73ff96882a0fb4d025ecc5669d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262e062dcdd2039084a356862b123e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/7/4/3015287038050304/3015557445787648/STEM/909052f3d060426bbb48fafc4d55a2da.png?resizew=168)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
5 . 如图所示,四棱锥
,底面在以AC为直径的圆O上,PO⊥圆O,
为等边三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/0e65482a-f13c-4612-8b1f-1c3a2afa045a.png?resizew=212)
(1)求证:平面PBD⊥平面PAB;
(2)线段PB上是否存在一点M使得直线PA与平面AMC所成角的正弦值为
?若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e89e99ab9c1ece0cc5c3bbabaa97de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/0e65482a-f13c-4612-8b1f-1c3a2afa045a.png?resizew=212)
(1)求证:平面PBD⊥平面PAB;
(2)线段PB上是否存在一点M使得直线PA与平面AMC所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55176f6357df50f85d36b732e31972d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b505e0df1131e3a93fc81d13f6e224e7.png)
您最近一年使用:0次
2022-05-07更新
|
544次组卷
|
3卷引用:福建省福安市第一中学2023届高三上学期第一次月考数学试题
名校
6 . 如图,在四棱锥
中,底面
为矩形,
,点
为线段
上的点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4999d4fbcbe15f78c29d518f25d317c2.png)
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970937448456192/2973101989535744/STEM/16e2fba3-b9d9-41b5-82ba-da6dda3a6bff.png?resizew=194)
(1)证明:
;
(2)若二面角
的大小为
,求直线
与平面
所成的角.
![](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/d9f48547d283e1459fe3c77e6249c8aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4999d4fbcbe15f78c29d518f25d317c2.png)
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970937448456192/2973101989535744/STEM/16e2fba3-b9d9-41b5-82ba-da6dda3a6bff.png?resizew=194)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d25b5ade550ec6afd3536e9eb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194add18a7df1a23cf1554dc2da1b40.png)
您最近一年使用:0次
2022-05-05更新
|
982次组卷
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6卷引用:福建省宁德市普通高中2022届高三五月份质量检测数学试题
解题方法
7 . 在棱长为1的正方体
,点B到平面
的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,底面ABCD为平行四边形,
平面ABCD,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968785218011136/2972215380320256/STEM/37a0f764e10a4be5b992cc8904386376.png?resizew=252)
(1)建立空间坐标系,写出平面PCD的一个法向量的坐标;
(2)若PB与平面ABCD所成角为30°,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/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968785218011136/2972215380320256/STEM/37a0f764e10a4be5b992cc8904386376.png?resizew=252)
(1)建立空间坐标系,写出平面PCD的一个法向量的坐标;
(2)若PB与平面ABCD所成角为30°,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65bf87f74420270138ed73a2d38ca48.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,四棱锥
的底面是矩形,
底面
,
,M为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942537856557056/2946224414875648/STEM/8b9407bf-ee47-4c2f-8196-4d9c7e989b43.png?resizew=185)
(1)求
长;
(2)求平面
的法向量
与
夹角
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d4d36ae30487030b827ce9413b9f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942537856557056/2946224414875648/STEM/8b9407bf-ee47-4c2f-8196-4d9c7e989b43.png?resizew=185)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
名校
解题方法
10 . 设
是两条不同的直线,
是两个不重合的平面,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2022-02-21更新
|
748次组卷
|
5卷引用:福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题
福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题江苏省盐城市东台创新高级中学2019-2020学年高一下学期4月检测数学试题(已下线)考点25 空间点、线、面的位置关系-备战2021年新高考数学一轮复习考点一遍过新疆乌鲁木齐地区2022届高三第一次质量监测数学(理)试题(问卷)宁夏石嘴山市第三中学2022届高三第一次模拟考试数学(理)试题