解题方法
1 . 在棱长为1的正方体
中,
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/1e9ca2ab-8a46-4210-84f2-cf2d5699ba8a.png?resizew=177)
(1)求二面角
的大小;
(2)求点
到平面
的距离;
(3)若点G是棱
上一点,当G在何处时,
平面
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505f8477b4a74dbeedff2163fef376a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348b35cc1233c9f83b5e2204a6beec4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/1e9ca2ab-8a46-4210-84f2-cf2d5699ba8a.png?resizew=177)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ddcf270cad9962145e0e75c8c7a57.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
(3)若点G是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
您最近一年使用:0次
2 . 如图,在棱长为2的正方体
中,点E是棱AB上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/e4b85639-19b3-4547-a169-a787fb7edd08.png?resizew=164)
(1)求证:
;
(2)点F、G分别是BC、CD的中点,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/e4b85639-19b3-4547-a169-a787fb7edd08.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b30478b45ea023eb5d23805aadf709.png)
(2)点F、G分别是BC、CD的中点,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695039ff24509ca88e5492f9f6b090f1.png)
您最近一年使用:0次
解题方法
3 . 已知向量
,
分别是直线
和平面
的方向向量和法向量,若
,则
与
所成角的大小是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e163480714acc9dae5005cac65d217d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6520a83186db32b24532316e6b62e2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
4 . 在如图所示的几何体
中,
面
,
面
,
,
,
为
的中点.
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0168e11ea64a82a3a7cc4bcf28a1dbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f09ad78d4eccd1a9c9ccd3c4af79c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c5ae16a7145a28a91d45ef950a07c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc8fdbe6cf2de964a6ac2c97b9fa90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fab827ebee09efe2dee1d7b6a4d6884.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-09-06更新
|
447次组卷
|
5卷引用:上海市崇明区横沙中学2023-2024学年高二上学期期末考试数学试题
上海市崇明区横沙中学2023-2024学年高二上学期期末考试数学试题广东省潮州市饶平县第二中学2020-2021学年高二下学期第一次月考数学试题河北省邯郸市大名县第一中学2022-2023学年高二上学期第一次月考数学试题广东省东莞市五校2022-2023年高二上学期期中联考数学试题(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
解题方法
5 . 如图,正方体
的棱长等于4,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/74bf211f-530e-4552-bcbb-007ff18d759b.png?resizew=150)
(1)求直线
与直线
所成的角;
(2)若底面
上的点
满足
平面
,求线段
的长度.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/74bf211f-530e-4552-bcbb-007ff18d759b.png?resizew=150)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
(2)若底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38278d5bacffa7f57ae741d431b72b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd7d2bc169d4467ad7d70861ed6351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
您最近一年使用:0次
解题方法
6 . 如图,已知点
在圆柱
的底面圆
上,
为圆
的直径,
、
为圆柱的母线,
,圆柱的体积为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/0add8cfc-bd60-40e4-a877-ac420fd852fd.png?resizew=150)
(1)求异面直线
与
所成角的大小(结果用反三角函数值表示);
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9c018281fcaaf52863e1f83d9dad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7798835dcf68ae8b8e61e2c38cf0839a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/0add8cfc-bd60-40e4-a877-ac420fd852fd.png?resizew=150)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36118a9e86f87ae75f554f8a3fcdb39d.png)
您最近一年使用:0次
7 . 在三棱锥
中,OA、OB、OC所在直线两两垂直,且
,CA与平面AOB所成角为
,D是AB中点,三棱锥
的体积是
.
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375692714270720/2376066405949440/STEM/aeb67cf4db314ff8a456671afa6920c5.png?resizew=152)
(1)求三棱锥
的高;
(2)在线段CA上取一点E,当E在什么位置时,异面直线BE与OD所成的角为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebc9b785a6bbb0ce1256a9e1ecc68f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fca3734de79f7f50b552ef62b29dc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebc9b785a6bbb0ce1256a9e1ecc68f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375692714270720/2376066405949440/STEM/aeb67cf4db314ff8a456671afa6920c5.png?resizew=152)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebc9b785a6bbb0ce1256a9e1ecc68f4.png)
(2)在线段CA上取一点E,当E在什么位置时,异面直线BE与OD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817c2109ca77615fa62754c71d1238f6.png)
您最近一年使用:0次
2020-01-13更新
|
133次组卷
|
2卷引用:2017年上海市崇明区高三第二次(4月)模拟数学试题