名校
1 . 如图,在直三棱柱
中,底面
为等腰直角三角形,
,
,
,
是侧棱
上一点,设
.
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852650345037824/2854469802041344/STEM/af56b6d5-6288-4888-b456-66ca73f49f9e.png?resizew=207)
(1)若
,求异面直线
与
所成角的大小;
(2)若
,求直线
与平面
所成角的大小;
(3)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d4b759e341f967a93fc478e795b72f.png)
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852650345037824/2854469802041344/STEM/af56b6d5-6288-4888-b456-66ca73f49f9e.png?resizew=207)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa575d601b92968dfcff972dfa111e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e753dc81ed21f878fff89e98cccf24a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db8814b2124793c2bdf3ea701fb14ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2021-11-19更新
|
218次组卷
|
3卷引用:上海市闵行(文琦)中学2021-2022学年高二上学期期中数学试题
2 . 如图,已知多面体
,
,
,
均垂直于平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852651028824064/2853489071775744/STEM/543f264c28d24d788a943f4c888d95e5.png?resizew=271)
(1)证明:
平面
;
(2)求直线
与平面
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d17d14819681c455a91d7678742368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc07af94c2ebedcab772b2b90ff1332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede14ef03dc3666b8a6902ddaf0021b6.png)
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852651028824064/2853489071775744/STEM/543f264c28d24d788a943f4c888d95e5.png?resizew=271)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e84d6e368f8368f8301c4cd66d6dd.png)
您最近一年使用:0次
名校
3 . 如图,四棱锥
的底面
是平行四边形,
底面
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e624e6ee68b796f70f9d35e78a8aed.png)
(2)若E是棱PC的中点,求直线AD与平面PCD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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e383629efd98f87ef95e1121fd8847c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e624e6ee68b796f70f9d35e78a8aed.png)
(2)若E是棱PC的中点,求直线AD与平面PCD所成的角
您最近一年使用:0次
2021-11-08更新
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1423次组卷
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10卷引用:黑龙江省鸡西实验中学2020-2021学年高一下学期期中考试数学试题
黑龙江省鸡西实验中学2020-2021学年高一下学期期中考试数学试题第13课时 课前 直线与平面垂直的性质(已下线)8.6 空间直线、平面的垂直(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)广东省清远市重点中学2021-2022学年高一下学期期中数学试题云南省昆明市嵩明县2021-2022学年高一下学期期中考试数学试题(已下线)8.6.2直线与平面垂直(第1课时)(练案)-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)广西南宁市宾阳中学2021-2022学年高一下学期期末考试数学试题安徽省滁州市定远县民族中学2021-2022学年高二下学期期末数学试题(已下线)高二上学期期中【常考60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)广东省韶关市韶实、榕城、清实、新河、龙实五校2023-2024学年高一下学期5月联考数学试题
4 . 如图,在三掕柱
中,
,
为
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827227211816960/2844597520375808/STEM/ea31f3d9d2fa4b2f82f0eee9d109515b.png?resizew=195)
(1)证明:
;
(2)已知四边形
是边长为2的菱形,且
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827227211816960/2844597520375808/STEM/ea31f3d9d2fa4b2f82f0eee9d109515b.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21478f83184c0f7577f8e24079abe381.png)
(2)已知四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
您最近一年使用:0次
5 . 如图,在四棱锥
中,
为
的中点,
为正三角形,底面
为直角梯形,
,
.在四棱锥
的平面展开图中,点
分别对应点
,
,
,
,且
,
,
三点共线,
,
,
三点共线,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/f659d907-562d-43f6-ae57-43946547bd91.png?resizew=421)
(1)证明:平面
平面
.
(2)设
,在棱
上是否存在一点
,使得
与平面
所成的角为
?若存在,求
;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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9460e8571262302490aca08902d67c4b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/f659d907-562d-43f6-ae57-43946547bd91.png?resizew=421)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dcf279d1756918052618fcb9b39107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f069fa1ce8a5cc587ec39d427e84d3c3.png)
您最近一年使用:0次
解题方法
6 . 如图,已知
是底面为正方形的长方体,
,
,点
是
上的动点
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/91aae9e6-34ef-4558-b606-90d6b533e84b.png?resizew=146)
(1)试判断不论点
在
上的任何位置,是否都有平面
垂直于平面
,并证明你的结论
(2)当
为
的中点时,求异面直线
与
所成角的余弦值;
(3)求
与平面
所成角的正切值的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489d8f964e1b16f6a9340fdab1a3b161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d125488e31956301c61d1ea1136f752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/91aae9e6-34ef-4558-b606-90d6b533e84b.png?resizew=146)
(1)试判断不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57043f1d131e9c7c8b71bf8a68bacbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ec06f50894c259172c934481b196b2.png)
您最近一年使用:0次
解题方法
7 . 在四棱锥P–ABCD中,底面ABCD是边长为6的正方形,PD平面ABCD,PD=8.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/5251c280-5f32-44cf-965d-cf88f43a890a.png?resizew=185)
(1)求异面直线PB与DC所成角的大小;
(2)求PA与平面PBD所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/5251c280-5f32-44cf-965d-cf88f43a890a.png?resizew=185)
(1)求异面直线PB与DC所成角的大小;
(2)求PA与平面PBD所成角的大小.
您最近一年使用:0次
8 . 如图,长方体中
中,
,点P为面
的对角线
上的动点(不包括端点),PN⊥BD于N.
![](https://img.xkw.com/dksih/QBM/2021/10/19/2832962918006784/2833684082114560/STEM/695b8c39fe9644769b9c4cdbbcf554c0.png?resizew=209)
(1)若点P是
的中点,求线段PN的长度;
(2)设
,将PN表示为
的函数,并写出定义域;
(3)当PN最小时,求直线PN与平面ABCD所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b98a13eacfcc6743aa433d7674e18e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://img.xkw.com/dksih/QBM/2021/10/19/2832962918006784/2833684082114560/STEM/695b8c39fe9644769b9c4cdbbcf554c0.png?resizew=209)
(1)若点P是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)当PN最小时,求直线PN与平面ABCD所成角的大小.
您最近一年使用:0次
2021-10-20更新
|
272次组卷
|
5卷引用:上海市宝山中学2021-2022学年高二上学期10月月考数学试题
上海市宝山中学2021-2022学年高二上学期10月月考数学试题上海师范大学第二附属中学2021-2022学年高二上学期期中数学试题上海市松江区第四中学2022-2023学年高二上学期期中数学试题(已下线)10.3 直线与平面所成的角 (第4课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020必修第三册)(已下线)期中真题必刷压轴60题(18个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
解题方法
9 . 如图所示,平面角为锐角的二面角
-EF-β,A∈EF,AG![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828926e570a414e9dbc04a7bbcb65283.png)
,∠GAE=45°,若AG与β所成角为30°,求二面角a-EF-β的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828926e570a414e9dbc04a7bbcb65283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/9c9368cb-7c4b-4074-8757-f5bb7d7542e8.png?resizew=219)
您最近一年使用:0次
名校
10 . 如图,在长方体
中,
点
分别在
棱上,且
,
.
![](https://img.xkw.com/dksih/QBM/2021/10/10/2826527973867520/2826597516083200/STEM/5e33727255384bc0bbc1ddac13a5a066.png?resizew=210)
(1)证明:
在同一个平面上;
(2)设直线
与平面
所成的角为
,直线
与平面
所成的角为
,判断
与
的大小关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3182a76f1a691c8ce96731f69c557d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b323ecfca28fb7da92643357158b3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b2e7cf650d04d4da289de3ed87634a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72169c29ddb8b22efe75d0c5775ee57.png)
![](https://img.xkw.com/dksih/QBM/2021/10/10/2826527973867520/2826597516083200/STEM/5e33727255384bc0bbc1ddac13a5a066.png?resizew=210)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de152b0c5f896197d4d2c7f7113276de.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
您最近一年使用:0次
2021-10-10更新
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801次组卷
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3卷引用:山东省潍坊市2021-2022学年高三上学期10月阶段性检测数学试题