名校
解题方法
1 . 如图,在四棱锥
中,
平面
,
,
,
,
,点
是
的中点.
;
(2)求直线
与平面
所成的角的余弦值.
![](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/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d6ee72557cb3c3830212d74bca615a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bc7e7906b002e1150680f6a67c30f4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
2023-09-18更新
|
714次组卷
|
7卷引用:广东省揭阳市普宁市第二中学2023-2024学年高三上学期第一次月考数学试题
广东省揭阳市普宁市第二中学2023-2024学年高三上学期第一次月考数学试题重庆市璧山来凤中学2023-2024学年高二上学期9月月考数学试题福建省泉州市晋江学校2023-2024学年高二上学期第一次阶段检测数学试题贵州省贵阳市观山湖区第一高级中学2023-2024学年高二上学期9月月考数学试题广东省茂名市高州中学2023-2024学年高二上学期12月月考数学试题江西省2024届高三第一次稳派大联考数学试题(已下线)专题06 用空间向量研究距离、夹角问题10种常见考法归类 - 【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)
2 . 《九章算术》中,将四个面都是直角三角形的四面体称为“鳖臑”,如图所示,四面体
中,
平面
,
,
是棱
的中点.
(1)判断四面体
是否为鳖臑,并说明理由;
(2)若四面体
是鳖臑,且
,求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/4c92d23c-f6d7-4450-b4ff-a587e7286502.png?resizew=146)
(1)判断四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8922620e649f55d79118cbabf947a8fa.png)
(2)若四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2479cd9055e57e504d64ea7d97e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-11-11更新
|
212次组卷
|
2卷引用:四川省南充市嘉陵第一中学2023-2024学年高二上学期12月月考数学试题
名校
3 . 设四边形
为矩形,点
为平面
外一点,且
平面
,若
,
.
(1)求
与平面
所成角的大小(用反三角函数表示);
(2)在
边上是否存在一点
,使得点
到平面
的距离为
,若存在,求出
的值,若不存在,请说明理由;
(3)若点
是
的中点,在
内确定一点
,使
的值最小,并求此时
的值.
![](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/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/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/94fb15c5-53e3-49b5-80e2-a53919943d90.png?resizew=200)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4180c271831327644dc83240b715b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c107850c8b505d853610d19e6ffbb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca14f6100d829f197a5dac5197bbe0b1.png)
您最近一年使用:0次
2023-11-10更新
|
398次组卷
|
2卷引用:上海市杨浦高级中学2023-2024学年高二下学期3月月考数学试卷
解题方法
4 . 如图,在空间直角坐标系中有长方体![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981564296ef340e41c91033abad4aa55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/843ea638-c873-4b67-8b0b-5bca0089b004.png?resizew=154)
(1)求
与面
所成角的正弦值
(2)求点B到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981564296ef340e41c91033abad4aa55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/843ea638-c873-4b67-8b0b-5bca0089b004.png?resizew=154)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcfe69b939fd1c271747fe9d37ccdf9.png)
(2)求点B到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,底面
是矩形,
平面
,
,
,点
,
分别为
,
的中点,且
.
的长;
(2)求直线
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/411b38a18046fea8e9fab1f9f9b80a5f.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/5fcac3b256b269b824d8738bb081f8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55bc62f8afd58b044a0c24bf361d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2023-10-13更新
|
345次组卷
|
7卷引用:山西省孝义市2023-2024学年高二上学期10月月考数学试题
6 . 在四棱锥S-ABCD中,底面ABCD为长方形,SB⊥底面ABCD,其中BS=2,BA=2,BC=λ,λ的可能取值为:①λ=
;②λ=
;③λ=
;④λ=
;⑤λ=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/ada8501f-20e8-4618-b8f2-9475e45ae2cc.png?resizew=147)
(1)求直线AS与平面ABCD所成角的正弦值.
(2)若线段CD上能找到点E,满足AE⊥SE,则λ可能的取值有几种情况?请说明理由.
(3)在(2)的条件下,当λ为所有可能情况的最大值时,线段CD上满足AE⊥SE的点有两个,分别记为
,求平面
与平面
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/ada8501f-20e8-4618-b8f2-9475e45ae2cc.png?resizew=147)
(1)求直线AS与平面ABCD所成角的正弦值.
(2)若线段CD上能找到点E,满足AE⊥SE,则λ可能的取值有几种情况?请说明理由.
(3)在(2)的条件下,当λ为所有可能情况的最大值时,线段CD上满足AE⊥SE的点有两个,分别记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500c66a44cd54c9c8d72e7a64eddbc31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971142e10d725c96be045dab5ecc59eb.png)
您最近一年使用:0次
7 . 如图,在正方体
中,点M,N,P,E,F分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/6b92fa9d-e2d1-4e45-bc75-e0d843356e76.png?resizew=174)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)求
与面
所成角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3062a2e1d37f6277b2627b560df51f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/6b92fa9d-e2d1-4e45-bc75-e0d843356e76.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d853e58bc8dd262f99df3827ead644f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52173c8cc44246823c2bee21a783b731.png)
您最近一年使用:0次
名校
8 . 如图,在三棱锥
中,侧棱
底面
,且
,过棱
的中点
,作
交
于点
,连接
.
(1)证明:
平面
;
(2)若
,三棱锥
的体积是
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1f69539b564b942e1133888643e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26260c10afb34f543d86b67898134f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/21/779893ef-997d-4ba3-95f8-0aea9823120b.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b115316e0fcd2ef46a4dd383472996e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2023-08-20更新
|
1287次组卷
|
5卷引用:湖南省长沙市第一中学2023-2024学年高三上学期月考(一)数学试题
湖南省长沙市第一中学2023-2024学年高三上学期月考(一)数学试题广西壮族自治区南宁市东盟中学2023-2024学年高二上学期开学考试数学试题(已下线)第02讲 空间向量的应用(2)(已下线)专题05 直线与平面的夹角4种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)第四章 立体几何解题通法 专题三 参数法 微点1 参数法(一)【培优版】
名校
解题方法
9 . 图①是由矩形
,
和菱形
组成的一个平面图形,其中
,
,
.将其沿
,
折起使得
与
重合,连接
,如图②.
平面
;
(2)证明:
//平面
;
(3)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d498a0467ff3c577a7ed175d7bffd885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da522aef3c452767df89b8d0eb62de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de93a4fa2069aed282b7a97a4b41afbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729c048c85a0c12eae9352dbe094dbcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693cd6179b2a92f03153ce12a0e86b95.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2023-08-02更新
|
532次组卷
|
5卷引用:山东省青岛市第五十八中学2022-2023学年高一下学期5月阶段性模块考试数学试题
山东省青岛市第五十八中学2022-2023学年高一下学期5月阶段性模块考试数学试题山东省威海市2022-2023学年高一下学期期末数学试题(已下线)8.6.3平面与平面垂直——课后作业(基础版)(已下线)重难点专题13 轻松搞定线面角问题-【帮课堂】(苏教版2019必修第二册)【人教A版(2019)】专题15立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
名校
10 . 如图,在直三棱柱
中,D为棱AB的中点,E为侧棱
的动点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09288c5259c905f6509051115f2d7ff1.png)
.
,使得
∥平面
?若存在,求出
的值;若不存在,请说明理由;
(2)设
,
,
,求DE与平面
所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09288c5259c905f6509051115f2d7ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8b50bf37cfd8cecf855ea7a817b0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f41d364b55d88688cd1f571ed231228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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