名校
1 . 如图,在正三棱柱
中,
为
中点,点
在棱
上,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
平面
;
(2)求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6d5a03b9a6918e8742a11a76aa4d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188e3f2275a92e2f4060d5a701bcb7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b887e16b95c673579030aadb147f930.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6b7921e70f73c845140f9428ed2af6.png)
您最近一年使用:0次
2024-05-09更新
|
1727次组卷
|
5卷引用:甘肃省兰州市西北师大附中2024届高三第五次诊断考试(三模)数学试题
解题方法
2 . 如图,在三棱锥
中,
平面
分别为
的中点,且
.
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41e8041cf64d835642a897f56b339a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1683fed718259fa7b77ced8be46c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a219cbad3454275ec748c3e00d535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f726924c16c769a012d7a111f81e44e7.png)
您最近一年使用:0次
名校
3 . 如图,在正方体
中,
,
分别为
,
的中点,点
在
的延长线上,且
.
平面
;
(2)求平面
与平面
的夹角的正切值.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6db8d970b9d4f6f55352c422fe777ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0df73a49d4348a5c1e3aaa149cc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
解题方法
4 . 如图,四棱锥
中,
底面
,
,
,
,
,
,
,
分别为
,
上一点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/be4a3708-c242-4865-881a-b628b9b5d02f.png?resizew=173)
(1)当
平面
时,求
的值;
(2)当二面角
的余弦值为
时,求
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c656a1d0532dd79ef1e61c807b7f6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933c8261064a77158575a037dbe94a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d459cad63e3cd2aba10862800fa4832.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/be4a3708-c242-4865-881a-b628b9b5d02f.png?resizew=173)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d25b5ade550ec6afd3536e9eb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
您最近一年使用:0次
5 . 已知直三棱柱
内接于球
,点
为
的中点,点
为侧面
上一动点,且
,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/e0301f429ebbcb3facf846bb0582d5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a485ce35e36e67861c1b8c424a3126.png)
A.点A到平面![]() ![]() |
B.存在点![]() ![]() ![]() |
C.过点![]() ![]() |
D.点![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图,在长方体
中,点
,
分别在棱
,
上,
,
,
,
.
.
(2)求平面
与平面
的夹角的余弦值.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25068e088bc3fc13c676fba0745825b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d27acdf2cbcb6dd59f532f8313ec629.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-12-19更新
|
834次组卷
|
8卷引用:甘肃省武威市2024届高三上学期阶段调考数学试题
名校
解题方法
7 . 如图,在四棱锥
中,
底面
,底面
是矩形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/655e8c62-2ec0-469f-8277-19bb2945eaff.png?resizew=154)
(1)证明:
.
(2)求二面角
的平面角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466deee706eb335b7d05b35bfc9319b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/655e8c62-2ec0-469f-8277-19bb2945eaff.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1269599d8f29c769773c8288e91b831.png)
您最近一年使用:0次
2023-03-24更新
|
1011次组卷
|
4卷引用:甘肃省兰州市第五十八中学2022-2023学年高三下学期第二次模拟考试数学(理科)试卷
名校
解题方法
8 . 在直三棱柱中,
,
,
,
,
,分别是
,
,
的中点,则下面说法中正确的有( )
A.![]() ![]() |
B.![]() |
C.直线![]() ![]() ![]() |
D.点![]() ![]() ![]() |
您最近一年使用:0次
2023-01-09更新
|
415次组卷
|
3卷引用:甘肃省兰州市第五十八中学教育集团2022-2023学年高三下学期2月建标考试数学(理科)试题
甘肃省兰州市第五十八中学教育集团2022-2023学年高三下学期2月建标考试数学(理科)试题福建省南安市侨光中学2022-2023学年高二上学期10月月考数学试题(已下线)通关练06 空间向量与立体几何章末检测(一)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
9 . 在正方体
中,
,
分别为
,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() ![]() | B.异面直线![]() ![]() |
C.平面![]() ![]() | D.平面![]() ![]() |
您最近一年使用:0次
2022-12-17更新
|
430次组卷
|
4卷引用:甘肃省张掖市某重点校2022-2023学年高三上学期12月月考数学(理)试题
甘肃省张掖市某重点校2022-2023学年高三上学期12月月考数学(理)试题(已下线)6.3.3空间角的计算(3)3.4向量在立体几何中的应用 测试卷-2022-2023学年高二上学期数学北师大版(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(1)
10 . 正方体
中,点
为线段
上的动点.
①当
为
的中点时,
面积最小;
②无论
在线段
的什么位置,均满足
;
③在线段
上存在一点
,使得
;
④三棱锥
的体积为定值.
以上正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4c381409a8d4bf6a9d65fbd23cec00.png)
②无论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c0e33b9d4ed545cd32c69e5f668b9f.png)
③在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e2d8f2ecd57a48f0645a0c8d9e5779.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a5001b1f0d8d89ed8e04607ac58ba.png)
以上正确结论的序号为
您最近一年使用:0次
2022-04-16更新
|
746次组卷
|
2卷引用:甘肃省2022届高三第二次高考诊断考试数学(理)试题