名校
解题方法
1 . 如图,四棱锥
中,底面
为四边形,
是边长为2的正三角形,
,
,
,平面
平面
,则( )
![](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/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a16dc02090b6e9263555061f14fbc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/80fa9699-4c08-42d1-87c6-0c98b943acc5.png?resizew=136)
A.![]() ![]() |
B.![]() |
C.![]() |
D.若二面角![]() ![]() ![]() |
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2023-06-22更新
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2卷引用:江苏省无锡市锡东高级中学2022-2023学年高一下学期5月月考数学试题
名校
2 . 如图,在多面体
中,平面
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/ee55d280-2694-4a53-9b85-dc10cb93c16c.png?resizew=200)
(1)求证:
;
(2)若四边形
为矩形,且
,求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a4e3f0349fa83dc2a0b7d798f04843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/ee55d280-2694-4a53-9b85-dc10cb93c16c.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5fd65265f85df7d149d83d80d4e62.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755b680b34589e9caa1920bf5a8d3258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
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名校
3 . 如图,在直三棱柱
中,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/f0a91814-d6e9-4911-a7d2-df3b7443fb25.png?resizew=133)
(1)求证:
;
(2)若
,平面
与平面
的夹角的大小是
与平面
所成角的大小的2倍,求侧棱BB1的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/f0a91814-d6e9-4911-a7d2-df3b7443fb25.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
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名校
4 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,D,E分别为
,
的中点,
,
,
.
平面
;
(2)在线段
上是否存在点F,使得平面
与平面
的夹角为
,若存在,求出
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
2023-04-30更新
|
2025次组卷
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6卷引用:江苏省无锡市辅仁高级中学2022-2023学年高一下学期期末数学试题
名校
解题方法
5 . 如图,已知长方体
中,四边形
为正方形,
,
,
,
分别为
,
的中点.则( )
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074832366305280/3075342447296512/STEM/2efc2a3c849742c69aa00b20b1e96ea7.png?resizew=222)
![](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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef8866ccf160ddc441bf69c5d3a3d5a.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074832366305280/3075342447296512/STEM/2efc2a3c849742c69aa00b20b1e96ea7.png?resizew=222)
A.![]() | B.点![]() ![]() ![]() ![]() |
C.直线![]() ![]() ![]() | D.三棱锥![]() ![]() |
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2022-09-27更新
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13卷引用:江苏省无锡市第一中学2021-2022学年高一艺术班下学期期中数学试题
江苏省无锡市第一中学2021-2022学年高一艺术班下学期期中数学试题福建省南安市柳城中学2021-2022学年高一下学期期中考试数学试题山东省青岛市青岛中学2022-2023学年高一上学期10月月考数学试题(已下线)6.4.1 平面几何中的向量方法(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)广东省广州市天河区2021届高考二模数学试题广东省广州市番禺区象贤中学2020-2021学年高二下学期期中数学试题广东省梅江市梅州中学2022届高三上学期10月月考数学试题湖南省长沙市雅礼中学2022届高三下学期月考(七)数学试题(已下线)第53讲 章末检测八江西省宜春市铜鼓中学2022-2023学年高二上学期第一次月考数学试题江苏省南京市建邺高中2022-2023学年高二上学期10月月考数学试题广东省肇庆市百花中学2022-2023学年高二上学期期中数学试题云南省宣威市第三中学2022-2023学年高二下学期第三次月考数学试题
6 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,
为
中点,
为
中点,
为线段
上一点.
为
中点,求证:
平面
;
(2)设直线
与底面
所成角的大小为
,二面角
的大小为
,若
,求
的长度.
![](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/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e076c4c39e0591ed69ff780fb5a1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5f8dfb22b415219ba7af3dc7e3d808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31388d7a9e6e86e51370879d23a8a6e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
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2022-07-02更新
|
735次组卷
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3卷引用:江苏省无锡市普通高中2021-2022学年高一下学期期末数学试题
名校
解题方法
7 . 正方体
中,下列叙述正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2021-08-17更新
|
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6卷引用:江苏省无锡市普通高中2019-2020学年高一下学期期末数学试题
江苏省无锡市普通高中2019-2020学年高一下学期期末数学试题江苏省无锡市锡东高级中学2023-2024学年高一下学期5月月考数学试卷重庆市凤鸣山中学2020-2021学年高一下学期期中数学试题江苏省南京航空航天大学苏州附属中学2020-2021学年高二上学期期初数学试题(已下线)第2讲 空间向量的应用-2021-2022学年高二数学多选题专项提升(人教A版2019选择性必修第一册)(已下线)1.4.2 用空间向量研究距离、夹角问题(同步练习)-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)
名校
解题方法
8 . 如图,在五面体
中,四边形
为正方形,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/2/25/2665512682430464/2668346601807872/STEM/0c4dd9d678b84050a904ec8525477ff9.png?resizew=189)
(1)若
,求二面角
的正弦值;
(2)若平面
平面
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f3df5713a423887c16e6355236372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11e72609ba0fbefe03c9f24165cbf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e0212491e4b2d7525de9a87fab3a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda0065dba34b90de18ad2d9009aefe3.png)
![](https://img.xkw.com/dksih/QBM/2021/2/25/2665512682430464/2668346601807872/STEM/0c4dd9d678b84050a904ec8525477ff9.png?resizew=189)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ade06068471a9d76e32b417bef7551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3832d29aa3ea504aa3bef7c87d62884.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
您最近一年使用:0次
2021-03-01更新
|
1329次组卷
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5卷引用:江苏省无锡市江阴市第一中学2020-2021学年高一下学期5月月考数学试题
江苏省无锡市江阴市第一中学2020-2021学年高一下学期5月月考数学试题江苏省盐城市、南京市2021届高三下学期第一次模拟考试数学试题(已下线)精做04 立体几何-备战2021年高考数学大题精做(新高考专用)湖北省新高考联考协作体2020-2021学年高二下学期期末数学试题(已下线)第1章 空间向量与立体几何-2021-2022学年高二数学课后培优练(人教A版2019选择性必修第一册)
名校
解题方法
9 . 四棱锥P-ABCD的底面是一个正方形,PA⊥平面ABCD,
,E是棱PA的中点,则异面直线BE与AC所成角的余弦值是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a4950a6e4202efd609507964af238b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/a1cf9b1b-e010-4668-9cfa-40276e305718.png?resizew=123)
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2020-10-14更新
|
440次组卷
|
2卷引用:江苏省无锡市江阴市第一中学2020-2021学年高一下学期5月月考数学试题
13-14高二下·四川内江·期末
名校
10 . 如图,在直三棱柱ABC﹣A1B1C1中,∠ACB
,D,E分别是AB,BB1的中点,且AC=BC=AA1=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/93cf35d0-3ce5-4404-86a1-f713e0fc2fe2.png?resizew=141)
(1)求直线BC1与A1D所成角的大小;
(2)求直线A1E与平面A1CD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894eb4e624079ad1d9aa1a5b30a38ba3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/93cf35d0-3ce5-4404-86a1-f713e0fc2fe2.png?resizew=141)
(1)求直线BC1与A1D所成角的大小;
(2)求直线A1E与平面A1CD所成角的正弦值.
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2020-01-21更新
|
570次组卷
|
6卷引用:江苏省无锡市天一中学2018-2019学年高一下学期期中考试数学(平行班)试题