名校
1 . 在四棱锥
中,
,
,
,
,
为正三角形,且平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894422649323520/2897144021975040/STEM/68d32b3d-3e68-4d14-a0a8-b707d27d9339.png?resizew=192)
(1)求二面角
的余弦值;
(2)线段PB上是否存在一点M(不含端点),使得异面直线DM和PE所成的角的余弦值为
?若存在,指出点M的位置;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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4622847599656e5684350af7e60f0d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45087cde2d66377517a3fce5553b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894422649323520/2897144021975040/STEM/68d32b3d-3e68-4d14-a0a8-b707d27d9339.png?resizew=192)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6aaed07f0b69eee41de11613fc74de.png)
(2)线段PB上是否存在一点M(不含端点),使得异面直线DM和PE所成的角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
您最近一年使用:0次
2022-01-18更新
|
2099次组卷
|
4卷引用:江苏省南通市如皋市2021-2022学年高二下学期期初调研数学试题
(已下线)江苏省南通市如皋市2021-2022学年高二下学期期初调研数学试题内蒙古包头市2021-2022学年高二上学期期末考试数学(理)试题内蒙古呼和浩特市新城区呼市十四中学2023-2024学年高二上学期期中数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
名校
2 . 如图,在四棱锥
中,平面
平面
,底面
是梯形,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893419281317888/2894108334833664/STEM/7d9e68773f8e4f328c5b8843e58d0de8.png?resizew=318)
(1)求证:
平面
;
(2)若直线
与平面
所成的角为30°,点
在线段
上,且
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65997b09d0cb2d4a7e46596c1a019e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d89e4d86a4305afd5784570a48435a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3580be24f1e4613f4fc16c768b537c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2783bb1b8182850d7bc1c175021a5d77.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893419281317888/2894108334833664/STEM/7d9e68773f8e4f328c5b8843e58d0de8.png?resizew=318)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77dca0e33db66ed5fcb6e5f797b99f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e3fbae2ae6e10ec068aa77ac33ed4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3142b1af4ce67d3e55417b4c0de257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
您最近一年使用:0次
2022-01-14更新
|
1221次组卷
|
5卷引用:6.3.3空间角的计算(备作业)-【上好课】2021-2022学年高二数学同步备课系列(苏教版2019选择性必修第二册)
(已下线)6.3.3空间角的计算(备作业)-【上好课】2021-2022学年高二数学同步备课系列(苏教版2019选择性必修第二册)河北省唐山市2021-2022学年高二上学期期末数学试题山西省太原师范学院附属中学2021-2022学年高二下学期开学测试(B卷)数学试题江西省抚州市临川第一中学2021-2022学年高二下学期第一次月考数学(理)试题河北省唐山市2022-2023学年高二上学期期末模拟数学试题
3 . 如图甲,直角梯形ABCD中,AB⊥AD,AD
BC,F为AD中点,E在BC上,且
,已知AB=AD=CE=2,现沿EF把四边形CDFE折起如图乙使平面CDFE⊥平面ABEF.
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758325185167360/2758421906546688/STEM/013735cb8c0f4544a918fd1711e1bfed.png?resizew=309)
(1)求证:
平面BCE;
(2)求证:平面ABC⊥平面BCE;
(3)求三棱锥C﹣ADE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758325185167360/2758421906546688/STEM/013735cb8c0f4544a918fd1711e1bfed.png?resizew=309)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
(2)求证:平面ABC⊥平面BCE;
(3)求三棱锥C﹣ADE的体积.
您最近一年使用:0次
2021-07-06更新
|
1301次组卷
|
3卷引用:13.3 空间图形的表面积和体积-2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)
(已下线)13.3 空间图形的表面积和体积-2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)江西省新余市2021-2022学年高一下学期期末考试数学试题江西省上高二中2022-2023学年高二上学期8月数学试题
名校
4 . 如图,以等腰直角
的斜边上的高AD为折痕,把
和
折成相互垂直的两个平面,下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505228143050752/2507095339827200/STEM/c66d82ec4ace488180ad837ba2a2c9a4.png?resizew=210)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505228143050752/2507095339827200/STEM/127f504463e3440faf7b4f11bb875996.png?resizew=282)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505228143050752/2507095339827200/STEM/c66d82ec4ace488180ad837ba2a2c9a4.png?resizew=210)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505228143050752/2507095339827200/STEM/127f504463e3440faf7b4f11bb875996.png?resizew=282)
A.![]() |
B.![]() |
C.若![]() ![]() |
D.二面角![]() ![]() |
您最近一年使用:0次
2020-07-16更新
|
1261次组卷
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5卷引用:江苏省苏州市第十中学2019-2020学年高一下学期期中数学试题
江苏省苏州市第十中学2019-2020学年高一下学期期中数学试题江苏省宿迁市宿豫中学2020-2021学年高三上学期第四次调研考试数学试题江苏省镇江市扬中市第二高级中学2020-2021学年高一下学期期末模拟数学试题(已下线)“8+4+4”小题强化训练(36)直线、平面垂直的判定与性质-2022届高考数学一轮复习(江苏等新高考地区专用)(已下线)考点35 空间几何体的表面积和体积(考点专练)-备战2021年新高考数学一轮复习考点微专题
名校
5 . 已知
,
是两条不重合的直线,
,
是两个不重合的平面,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
您最近一年使用:0次
2021-08-09更新
|
583次组卷
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3卷引用:江苏省南通市2020-2021学年高一下学期期末数学试题
江苏省南通市2020-2021学年高一下学期期末数学试题(已下线)专题8.4 直线、平面平行的判定及性质(练)- 2022年高考数学一轮复习讲练测(新教材新高考)甘肃省张掖市某重点校2022-2023学年高三上学期期中检测数学(理)试题
名校
6 . 如图,在三棱锥
内,侧面
底面
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2039a31f9775d806039d640499ddb2.png)
,则
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399ac4b2538752751cf2e54d11813308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2039a31f9775d806039d640499ddb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a4c0a72ac0087bb8e43528afa13f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c80c9ed64d09ebe5fc863748c84638d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/25e0cd98-e705-42ff-b73b-110cbfbc80aa.jpg?resizew=169)
您最近一年使用:0次
2019-05-23更新
|
1152次组卷
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9卷引用:【新教材精创】13.2.4平面与平面的位置关系—两平面垂直的判定与性质学案
(已下线)【新教材精创】13.2.4平面与平面的位置关系—两平面垂直的判定与性质学案步步高高二数学暑假作业:【文】作业13 点、直线、平面之间的位置关系(已下线)【新教材精创】11.4.2平面与平面垂直(第2课时)练习(1)(已下线)【新东方】绍兴qw119北师大版(2019) 必修第二册 金榜题名 第六章 立体几何初步 §5 垂直关系 5.2 平面与平面垂直广东省顺德市李兆基中学2019-2020学年高二上学期10月月考数学试题第二章 第三节 2.3直线、平面垂直的判定及其性质(已下线)8.6.3平面与平面垂直(练案)-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)(已下线)8.6.3平面与平面垂直【第一课】“上好三节课,做好三套题“高中数学素养晋级之路
名校
7 . 已知直线
、
与平面
、
,
,
,则下列命题中正确的是_______ (填写正确命题对应的序号).
①若
,则
②若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
③若
,则
④若
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f157205cb5cb4a538b09d989f2d9ae95.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daef06d98295115dca121cb7647e7bc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de666db0febae223cc4d1dc189d71ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dedfa42c16dd0aefa2928a6e41f3dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d8dcd07ffe20d7b6241d50eed2f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5986f2991d45fbf3578f08f27d9fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe920cd78db25f5b4df37d066e57800.png)
您最近一年使用:0次
2019-01-08更新
|
921次组卷
|
10卷引用:【市级联考】江苏省南京市13校2019届高三12月联合调研测试数学试题
【市级联考】江苏省南京市13校2019届高三12月联合调研测试数学试题(已下线)专题8.5 直线、平面垂直的判定及其性质(练)-浙江版《2020年高考一轮复习讲练测》湖南省衡阳市衡阳县2018-2019学年高二下学期六科联赛数学(理)试题甘肃省静宁县第一中学2020届高三第七次模拟考试数学(理)试题甘肃省静宁县第一中学2020届高三第七次模拟考试数学(文)试题(已下线)专题8.5 直线、平面垂直的判定及性质(练)-2021年新高考数学一轮复习讲练测(已下线)第29练 空间点、线、面的位置关系-2021年高考数学(文)一轮复习小题必刷陕西省西安中学2021届高三高考数学(理)模拟试题(三)安徽省滁州市定远县育才学校2021届高三下学期开学考试数学(文)试题广东省梅州市兴宁市东红中学2021届高三下学期期中数学试题
8 . 如图,在矩形
中,
,
为
中点,沿直线
将
翻折成
,使平面
平面
.点
分别在线段
上,若沿直线
将四边形
向上翻折,使
与
重合,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7277d4fa62666459e91b0f16f3756c65.png)
__________ ,四棱锥
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391573c30964b87ca3429bf67ae22aa.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b12cffc313a181f666e3fc8e66b6f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a832b538d0bd5a0051d485fae371a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3956369191d0383bdb8786134da7dd9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fbd6d40dc152a39905d3ed13420a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7277d4fa62666459e91b0f16f3756c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7df0b6da943f3bbe684ac94c5fa7cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/a87dc48d-831e-4b5f-a2e6-5cf188e35da8.png?resizew=247)
您最近一年使用:0次
2020-05-05更新
|
544次组卷
|
2卷引用:江苏省苏州市2022届高三下学期3月模拟数学试题
9 . 如图,在四棱锥
中,平面
平面
,四边形
为矩形,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/66ba14d2-a410-4013-9688-88c2c9f09d64.png?resizew=194)
(1)求证:
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/66ba14d2-a410-4013-9688-88c2c9f09d64.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5f8d21c0db7f57ad223a2db0e73bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
10 . 如图,在△ABC中,∠B=90°,AB=BC=2,P为AB边上一动点,PD∥BC交AC于点D,现将△PDA沿PD翻折至△PDA1,E是A1C的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/68cb8ec0-496c-47cf-bfc7-4b066d0fae17.png?resizew=160)
(1)若P为AB的中点,证明:DE∥平面PBA1.
(2)若平面PDA1⊥平面PDA,且DE⊥平面CBA1,求四棱锥A1﹣PBCD的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/68cb8ec0-496c-47cf-bfc7-4b066d0fae17.png?resizew=160)
(1)若P为AB的中点,证明:DE∥平面PBA1.
(2)若平面PDA1⊥平面PDA,且DE⊥平面CBA1,求四棱锥A1﹣PBCD的体积.
您最近一年使用:0次
2019-10-14更新
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624次组卷
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8卷引用:期末综合检测05-2020-2021学年高一数学下学期期末专项复习(苏教版2019必修第二册)
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