名校
1 . 在四棱锥
中,底面
是正方形,
底面
,
,截面
与直线
平行,与
交于点
,则下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6be2cf63-6c8f-44b4-9295-5264406558b2.png?resizew=166)
![](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/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6be2cf63-6c8f-44b4-9295-5264406558b2.png?resizew=166)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.三棱锥![]() ![]() ![]() |
您最近一年使用:0次
2021-07-19更新
|
2205次组卷
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25卷引用:山东省威海市乳山市银滩高级中学2022-2023学年高二上学期12月月考数学试题
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2 . 在棱长为2的正方体
中,点P满足
,其中
,
.当直线
平面
时,P的轨迹被以
为球心,R为半径的球面截得的长度为2,则R=______ ;当
时,经过A,
,P的平面与棱
交于点Q,则直线PQ与平面
所成角的正切值的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545017eee79a71befee621b52c8cae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6813066ab6672e10749e502ff8dc702f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf58a9fc561ffdbd1f982b4aa949d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
您最近一年使用:0次
名校
解题方法
3 . 在三棱柱
中,侧面正方形
的中心为点
平面
,且
,点
满足
.
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
,求
的值;
(2)求点
到平面
的距离;
(3)若平面
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c08f5ff21be00a3ce445b52db40a322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3d67dce9e64e8ef0c6d0d639eaa919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e6a0e4b373d19703438f79261c469a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/19/64db6f6c-97e8-4c27-9db3-a6cbbc0371a5.png?resizew=226)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b886daa3c9bb7153acd9f651f99eb2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b886daa3c9bb7153acd9f651f99eb2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-01-26更新
|
1000次组卷
|
8卷引用:山东省威海市2021-2022学年高二上学期期末数学试题
解题方法
4 . 在正方体
中,
,
,
分别为
,
,
的中点,
为底面
上一动点,且直线
平面
,则
与平面
所成角的正切值的取值范围为( )
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0875cc63101ea9c8a7ad19a94bd6d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 已知正方形
的边长为
,沿
将三角形
折起到
位置(如图),
为三角形
的重心,点
在边
上,
平面
.
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640253283827712/2643603612114944/STEM/bdacd9a2-cf9d-4426-a81d-4c12c79c3cac.png?resizew=429)
(1)若
,求
的值;
(2)若
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a227bcc7ee91e914c0c6bec05f82b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640253283827712/2643603612114944/STEM/bdacd9a2-cf9d-4426-a81d-4c12c79c3cac.png?resizew=429)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826ad035e65e10b67080ed3177bcd8e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270bd4bc3667aeb3347e0982b5f586da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6734b2bef8750392d3c5c08b5d878505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2021-01-25更新
|
315次组卷
|
2卷引用:山东省威海市乳山市第一中学2022-2023学年高二上学期12月月考数学试题
6 . 如图,在以
为顶点的五面体中,四边形
为正方形,
.
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525062377422848/2528290386165760/STEM/8fb77e02-61e0-414d-8ae5-d5170e6ed511.png)
(1)证明:平面
平面
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63a98f5ed97655875ffb3f9eb413d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e8903fed7c27fcba13f00819b869a1.png)
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525062377422848/2528290386165760/STEM/8fb77e02-61e0-414d-8ae5-d5170e6ed511.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6240d4cf0fb44aa1e6bdaf2a4bdfb37e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd8a97f37156cec6592795da3941f87.png)
您最近一年使用:0次
解题方法
7 . 如图,三棱柱
的各棱长均相等,
底面
,E,F分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/beb89dfc-6c25-41f0-969d-a7ce35baddcf.png?resizew=200)
(1)过
作平面
,使得直线
平面
,若平面
与直线
交于点H,指出点H所在的位置,并说明理由;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cf3bff56a7f4ab6c0008e90823025d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3073a50d7c1b9b4d6e213576c42c2d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469afb06bd2d87d2aef9da9f43117bee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/beb89dfc-6c25-41f0-969d-a7ce35baddcf.png?resizew=200)
(1)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca622ed14d88fffeff480e373423d0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5e50bf09ceadd1715cd1265b5477a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5e50bf09ceadd1715cd1265b5477a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5e50bf09ceadd1715cd1265b5477a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86814dbae9a5343d69bb4647900b3bfe.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebdd2e8204efbd6f623012a0427f148.png)
您最近一年使用:0次
2018-04-25更新
|
680次组卷
|
2卷引用:山东省威海市乳山市银滩高级中学2023-2024学年高二上学期12月月考数学试题
8 . 如图,在以
为顶点的五面体中,面
为正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525062268846080/2528266344062976/STEM/34c8202b340549208f170637c3a8cc09.png?resizew=260)
(1)证明:平面
平面
;
(2)证明:
;
(3)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63a98f5ed97655875ffb3f9eb413d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6805884ba9da24759ff418d7a98db2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0e38c274227cbc24bda9ecb457ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f233c56cf87c12812fc569e0147c8f0.png)
![](https://img.xkw.com/dksih/QBM/2020/8/10/2525062268846080/2528266344062976/STEM/34c8202b340549208f170637c3a8cc09.png?resizew=260)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6240d4cf0fb44aa1e6bdaf2a4bdfb37e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451557ef624a9c142ebc5fa155e0e28b.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
14-15高一上·山东威海·期末
9 . 定理:如果一条直线和一个平面平行,经过这条直线的平面和这个平面相交,那么这条直线就和两平面的交线平行.
请对上面定理加以证明,并说出定理的名称及作用.
请对上面定理加以证明,并说出定理的名称及作用.
您最近一年使用:0次
解题方法
10 . 在正方体
中,E,F分别为棱BC,
的中点,若平面
与平面
的交线为l,则l与直线
所成角的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e3ece4dce20324f55badd3d9225e19.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次