名校
1 . 在如图所示的多面体
中,四边形
是边长为
的正方形,其对角线的交点为
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b695b7f6cade157f08afee8570804e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84da16fb63c603c1a4383e83a97787f4.png)
,点
是棱
的中点.
平面
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee947130b72cccc577463e7c3d6e46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1c2a9af60eeffad1df194e21aa08ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b695b7f6cade157f08afee8570804e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84da16fb63c603c1a4383e83a97787f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70ba19e25c0ee0e174e72ba192834c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8948ac8156d19336083987d47b0f7038.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
您最近一年使用:0次
7日内更新
|
414次组卷
|
2卷引用:黑龙江省部分学校2023-2024学年高三第三次模拟数学试题
名校
解题方法
2 . 已知四棱锥
的底面
是棱长为2的菱形,
,若
,且
与平面
所成的角为
为
的中点,点
在线段
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
平面
.
;
(2)求平面
与平面
夹角的大小.
![](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/2996d02ef58faec7918d55e5e7a59860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27dd7473bc61f631d788b152b16363f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad573edaad2b4dc616a0a3eb1fc92f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b2857b27a9ac7c6c9f87f6217caa49.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在直三棱柱
中,
,
,
分别为
,
的中点.
平面
;
(2)线段
上是否存在点
,使得直线
与平面
所成的角的正弦值为
,若存在,求出线段
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4070c1fa8bdb6a934b55c5b2bedd035b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d4548c32861ade058b139a5b2ec801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2024-06-12更新
|
240次组卷
|
2卷引用:黑龙江省哈尔滨市第二十四中学校2024届高三下学期第三次模拟测试数学试题
4 . 如图,三棱柱
中,侧面
为矩形,
,
,底面
为等边三角形.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/844b54fac727753d81a6be086330c9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fea64ed589e56f11d34e8a1c120a08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04a2f09a6d56ce328f0fa843ef8fa89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
2024-06-11更新
|
562次组卷
|
3卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试(二)数学试题
名校
解题方法
5 . 如图,四棱锥
的底面
是矩形,
平面
为
的中点,
为PA上一点,且
.
平面BDQ;
(2)若二面角
为
,求三棱锥
的体积.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19210d688c39eb13fdf214dc517b1556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571c3a99cf0b5225444cc5d2d586874d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2386b1cb84295ef95039af00cc76772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ccef06bd7c89746239123517347c3.png)
您最近一年使用:0次
2024-06-11更新
|
170次组卷
|
2卷引用:黑龙江省双鸭山市第一中学2024届高三下学期第五次模拟考试数学试卷
名校
6 . 如图,在四棱锥
中,底面
是正方形,
底面
,
.
为
中点,求证:
平面
;
(2)求平面
与平面
的夹角.
![](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/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3bd9c2db8c9f3cb8c6c7d7cbf5465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
您最近一年使用:0次
2024-06-04更新
|
1751次组卷
|
4卷引用:黑龙江省牡丹江市第三高级中学2024届高三下学期高考前适应性演练数学试卷
黑龙江省牡丹江市第三高级中学2024届高三下学期高考前适应性演练数学试卷安徽省江淮十校2024届高三第三次联考数学试题(已下线)6.4 空间向量与立体几何(高考真题素材之十年高考)2海南省部分学校2024届新高考二卷押题卷(三)数学试题
名校
解题方法
7 . 在正四棱柱
中,
.
上是否存在一点
,使得直线
平面
,若存在,求出
长,若不存在,请说明理由;
(2)已知点
在线段
上,且
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6313a1a76310f15d271421c1f0d3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f36f074d1dc1054c679236ec70dcaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4500272aa458afeeb2fb8fff527c8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42c0009e041ac9af518f5a9efbb7d19.png)
您最近一年使用:0次
名校
解题方法
8 . 已知圆柱
,
,
分别是上下底面的直径,
,
是两条母线,E为下底面
上一动点.
平面
;
(2)若E弧
上为靠近A的三等分点,F为
的中点,底面半径为2,高为4,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若E弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6eef5161fff77cef69133326c1739d.png)
您最近一年使用:0次
名校
解题方法
9 . 如图:四棱柱
底面
为等腰梯形,
.
平面
;
(2)若
为菱形,
,平面
平面
.
①求平面
和平面
夹角的余弦;
②求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146852cf67ba9571582e9ed8a1c6d1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44edb46eb17d224e0d9a2667c2e5df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe2d3e28cc6b7f4454f4123a5217513.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c916c3d694edd86863a205d95a6648e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe2d3e28cc6b7f4454f4123a5217513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0ca7c25eceffc1c3515446f59396e1.png)
②求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe2d3e28cc6b7f4454f4123a5217513.png)
您最近一年使用:0次
10 . 如图,在正三棱柱
中,
,点
为
的中点.
//平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da7fd8e46e7db2d692486c252274cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次