名校
解题方法
1 . 如图,在四棱锥P-ABCD中,底面ABCD为菱形,E为棱AB的中点,AC⊥PE,PA=PD.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/df736301-4b5d-4bb5-9fd9-04ea9122b7f9.png?resizew=177)
(1)证明:平面PAD⊥平面ABCD;
(2)若PA=AD,∠BAD=60°,求二面角
的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/df736301-4b5d-4bb5-9fd9-04ea9122b7f9.png?resizew=177)
(1)证明:平面PAD⊥平面ABCD;
(2)若PA=AD,∠BAD=60°,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abca0f7f7f2f49d821be607579565963.png)
您最近一年使用:0次
2023-12-20更新
|
1212次组卷
|
12卷引用:江苏省苏州市部分学校2024届高三上学期第二次调研考试数学试题
江苏省苏州市部分学校2024届高三上学期第二次调研考试数学试题东北三省三校2023届高三第一次联合模拟考试数学试题(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题江西省新余市2023届高三二模数学(理)试题(已下线)2023年高考数学(理)终极押题卷陕西师范大学附属中学2022-2023学年高二下学期期末理科数学试题云南省昆明市官渡区尚品书院学校2022-2023学年高二下学期3月月考数学试题黑龙江省饶河县高级中学2022-2023学年高二下学期第一次月考数学试题(已下线)专题13 空间向量的应用10种常见考法归类(2)辽宁省沈阳市五校协作体2023-2024学年高二上学期期末考试数学试题河南省南阳市桐柏县2023-2024学年高二上学期期末质量检测数学试题
名校
2 . 在正三棱柱
中,
,
,E,F分别是棱BC,AC上的动点(不包括端点),且满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68004768b879c6a052f45a2c45217cd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/27/0e12d19e-9c82-4832-932d-dcc621008ba9.png?resizew=164)
A.存在点E,使得![]() | B.直线![]() ![]() |
C.三棱锥![]() ![]() | D.二面角![]() |
您最近一年使用:0次
名校
3 . 如图,在三棱柱
中,四边形
为正方形,点
为棱
的中点,平面
平面
,
.
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98413205ebd1c689855bd6ba189156c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/26/f214f08f-cdf5-4e0b-9da4-436b8c95f2e3.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5d4a7095f454961da088fd86f1b556.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b935580f6c20b82112df78d570a482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b21e7935f3dfb2488278984776a738.png)
您最近一年使用:0次
2023-05-25更新
|
776次组卷
|
4卷引用:江苏省盐城市2023届高三三模数学试题
2023·江苏南通·模拟预测
名校
解题方法
4 . 在三棱锥
中,
平面
,
,
,
,
,点M在该三棱锥的外接球O的球面上运动,且满足
,则三棱锥
的体积最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2574b6b77481c7b1c0be9148f6905dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e621c984c64e8008d43c867bb22768ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b9ddeedeff87f7722aedd6c1109d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70e9a28e85ccb37507499c56eff84d2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 在梯形
中,
,
,
,
,如图1.现将
沿对角线
折成直二面角
,如图2,点
在线段
上.
;
(2)若点
到直线
的距离为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cfd06965af6014208127f2880b476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ac7094262811e033da37dd18ed8b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b925e994247985e948757354d63ace2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8180b12d96caf2e6b3ca28a474185e41.png)
您最近一年使用:0次
2023-05-05更新
|
1866次组卷
|
6卷引用:江苏省南京市2023届高三二模数学试题
江苏省南京市2023届高三二模数学试题(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)第11讲 第一章 空间向量与立体几何 章末题型大总结(2)(已下线)考点11 空间距离 2024届高考数学考点总动员 【讲】(已下线)专题06 立体几何 第一讲 立体几何中的证明问题(解密讲义)(已下线)第33题 空间距离解法笃定,向量方法建系第一(优质好题一题多解)
名校
6 . 如图,在四棱锥
中,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/76440198-7fbb-4295-8612-011124ae8440.png?resizew=156)
(1)证明:
平面
;
(2)若
是
的中点,
,
.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/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d390782b8ea7016628ee68403dcbfbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746f70c9993f04a5037c53daf3d1af00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/76440198-7fbb-4295-8612-011124ae8440.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bee9d35f57e7bd81f397f82a34bbc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de3595bb7c79503fabd75d99196ccb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
2023-03-26更新
|
767次组卷
|
2卷引用:江苏省南京师范大学附属中学江宁分校等2校2023届高三一模数学试题
名校
解题方法
7 . 在三棱锥
中,
两两垂直,
,
为棱
上一点,
于点
,则
面积的最大值为______ ;此时,三棱锥
的外接球表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6927ad225f9569644196cd01ab9ef0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e344965c28b5303bb0929232bf651e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19dd332eccf6ca418898e64b3a1f583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0756277c18bea4e9c3b74fb28fd58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2e3cac5106bc8a7ad98618c251cb5d.png)
您最近一年使用:0次
2023-03-24更新
|
2509次组卷
|
8卷引用:江苏省南京市临江高级中学2023届高三下学期二模拉练数学试题
江苏省南京市临江高级中学2023届高三下学期二模拉练数学试题山东省烟台市2023届高三一模数学试题山东省德州市2023届高考一模数学试题(已下线)“8+4+4”小题强化训练(21)(已下线)专题09 立体几何初步贵州省黔西南州兴义市第六中学2022-2023学年高二下学期期中检测数学试题江苏省连云港市灌云高级中学2024届高三上学期期末数学试题(已下线)第四章 立体几何解题通法 专题三 参数法 微点1 参数法(一)【培优版】
名校
解题方法
8 . 在直角梯形
中,
,
,
,E为
的中点.将
和
分别沿
折起,使得点A,D重合于点F,构成四面体
.若四面体
的四个面均为直角三角形,则其外接球的半径为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7c4762381fa5fb173866d31b749d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82fd2c740aea7423ecc2077ed899260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9f9f6dd9ba701b84aa9ad357c99e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9f9f6dd9ba701b84aa9ad357c99e3d.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,侧棱
矩形
,且
,过棱
的中点
,作
交
于点
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073fc51a00b25cb6ddf7b621a556ea4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/b856c107-3cbe-4e3c-899d-6b914aad0734.png?resizew=171)
(1)证明:
;
(2)若
,平面
与平面
所成二面角的大小为
,求
的值.
![](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/37e2267c84394668eff2e9f5918de4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073fc51a00b25cb6ddf7b621a556ea4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/b856c107-3cbe-4e3c-899d-6b914aad0734.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c3c17bd1521549221a9c1c1ca33d0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dd7ed07ca176565adeba7073634dce.png)
您最近一年使用:0次
2023-03-10更新
|
3742次组卷
|
6卷引用:江苏省南京师范大学附属中学2022-2023学年高三一模适应性考试数学试题
名校
解题方法
10 . 在三棱锥
中,
,且
,则直线PC与平面ABC所成角的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee9af801681f81782111e26ca6e7dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc53c3471aac39eaf29c80a319800fc4.png)
您最近一年使用:0次
2023-03-07更新
|
838次组卷
|
3卷引用:江苏省徐州市沛县2023-2024学年高三上学期期初模拟测试(一)数学试题