名校
1 . 如图,四面体
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/4a6ecf0e-7c53-4ebd-b52c-7e165a429b2d.png?resizew=151)
(1)求直线
与平面
所成角的大小;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/4a6ecf0e-7c53-4ebd-b52c-7e165a429b2d.png?resizew=151)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
名校
2 . 如图所示,已知
中,
,且
,现将
沿BC翻折到
,满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/f09d95aa-931b-44c6-92f7-b6c12621c71e.png?resizew=146)
(1)求证:
;
(2)若E为边CD的中点,求直线AE与平面ABC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc223bc59d4c5b1c99f811e4bded9783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f278de55bd20ebbebf93b2bffa77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9b12026eb766b2066b95cdc41220a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/f09d95aa-931b-44c6-92f7-b6c12621c71e.png?resizew=146)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
(2)若E为边CD的中点,求直线AE与平面ABC所成角的正弦值.
您最近一年使用:0次
2023-02-22更新
|
695次组卷
|
6卷引用:10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)
(已下线)10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)北京市清华大学THUSSAT2023届高三上学期12月诊断性测试数学(理)试题中学生标准学术能力诊断性测试2022-2023学年上学期12月测试(新课改版)数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题17-22(已下线)专题20 空间几何解答题(文科)-1(已下线)专题8.15 空间中线面的位置关系大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
名校
解题方法
3 . 如图,正四棱柱
中,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/74edd663-1823-4694-9191-01b7a278ad70.png?resizew=170)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/74edd663-1823-4694-9191-01b7a278ad70.png?resizew=170)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554923047631d16320c2ba39abeee99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6606c156191bde3dc2309975f47f4b8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6606c156191bde3dc2309975f47f4b8.png)
您最近一年使用:0次
2023-02-22更新
|
480次组卷
|
9卷引用:上海市青浦高级中学2022届高三下学期3月月考数学试题
上海市青浦高级中学2022届高三下学期3月月考数学试题黑龙江省哈尔滨市第六中学2020-2021学年高一下学期期末考试数学试题(已下线)专题1.11 空间向量与立体几何大题专项训练(30道)-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)1.4空间向量的应用(专题强化卷)-2021-2022学年高二数学课堂精选(人教版A版2019选择性必修第一册)广东省深圳外国语学校2022届高三下学期第二次检测数学试题(已下线)第08讲 第七章 立体几何与空间向量(基础拿分卷)福建省三明第一中学2022-2023学年高二上学期期中考试数学试题重庆市第十八中学2023届高三下学期二月开学检测数学试题新疆伊犁哈萨克自治州奎屯市第一高级中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
4 . 如图,在棱长为
的正方形ABCD中,E,F分别为CD,BC边上的中点,现以EF为折痕将点C旋转至点P的位置,使得
为直二面角.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/140f0e32-f2fa-468d-bdf2-5e872379e495.png?resizew=310)
(1)证明:
;
(2)求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13259de331de43dda25f2688b7822663.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/140f0e32-f2fa-468d-bdf2-5e872379e495.png?resizew=310)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2484662ae40c406b054d14a7f9e118.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
您最近一年使用:0次
2023-02-21更新
|
672次组卷
|
8卷引用:10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)
(已下线)10.3 直线与平面间的位置关系(第3课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)2019届百师联盟全国高三模拟考(三)全国 I 卷数学(理)试题2019届百师联盟全国高三模拟考(三)全国 I 卷文科数学试题山西省吕梁市孝义市2023届高三上学期期末模拟数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题17-22(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)甘肃省天水市第一中学2022-2023学年高二下学期3月月考数学试题安徽省淮北市树人高级中学2023-2024学年高二上学期开学检测数学试题
21-22高三上·上海浦东新·期中
名校
解题方法
5 . 如图,在正三棱柱
中,
点
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/997a78f2-b661-46bc-bbd6-bef587a0f1c1.png?resizew=152)
(1)求异面直线
与
所成角的大小;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/997a78f2-b661-46bc-bbd6-bef587a0f1c1.png?resizew=152)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc96c20ebba91031a1c54037fe651c.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在正四棱锥
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/82bcdba8-2538-4068-83c3-4a3c62eefec5.png?resizew=188)
(1)求侧棱
与底面ABCD所成角的大小;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06cb01443be899ef03dfe279af2ecfa2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/82bcdba8-2538-4068-83c3-4a3c62eefec5.png?resizew=188)
(1)求侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
您最近一年使用:0次
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7 . 如图,在正方体
中,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/07d19797-1c93-44dd-9a28-f81b2bf0c917.png?resizew=186)
(1)求:异面直线
与
所成角的大小;
(2)求:直线
与平面
所成角的正弦值.
![](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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/07d19797-1c93-44dd-9a28-f81b2bf0c917.png?resizew=186)
(1)求:异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
解题方法
8 . 如图,在直角
中,
,斜边
,
是
中点,现将直角
以直角边
为轴旋转一周得到一个圆锥.点
为圆锥底面圆周上一点,且
.
(2)求直线
与平面
所成的角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991c8373be20b4325ba779e4dfdc8b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cb551de43a9c1967e3f36f79480be6.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa3a310c1f8a5af35dc3328d874e18e.png)
您最近一年使用:0次
2023-01-11更新
|
585次组卷
|
5卷引用:上海市浦东新区2022-2023学年高二上学期期末数学试题
上海市浦东新区2022-2023学年高二上学期期末数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)13.2.3 直线和平面的位置关系(1)(已下线)专题10 空间角与空间距离的综合(1)-期中期末考点大串讲(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题17-21
名校
解题方法
9 . 《九章算术》中,将四个面都是直角三角形的四面体称为“鳖臑”,如图所示,四面体
中,
平面
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/2d31a773-af75-42ec-a600-c3fec4225421.png?resizew=121)
(1)证明:
,并判断四面体
是否为鳖臑?若是,写出其每个面的直角;若不是,说明理由;
(2)若四面体
是鳖臑,且
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b13c6f183014d6ab494637f3eb71ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/2d31a773-af75-42ec-a600-c3fec4225421.png?resizew=121)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c71dbf267939080668be464f1aa60da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f75a61b196a214cc40bb054d21a74a6.png)
(2)若四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2479cd9055e57e504d64ea7d97e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
解题方法
10 . 在直三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/557b9f31-09a7-4977-86d3-b9258964561a.png?resizew=161)
(1)求四棱锥
的体积V;
(2)求直线
与平面
所成角的大小;
(3)求异面直线
与
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96a6b20a35af7755e5d90789ea862da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/557b9f31-09a7-4977-86d3-b9258964561a.png?resizew=161)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d0727de4c16b53b4bb6ab370afde6c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(3)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次