名校
1 . 如图,已知四棱锥
中,
平面
,平面
平面
,且
,
,
,点
在平面
内的射影恰为
的重心
.
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efeadd146662b5d8fe14a424138ef751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beb1af9d2ffb7d0089dec2c1af554da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f944f78358763be992bb3d55fff12f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/be9f0415-67d9-41e0-9e15-0bdea568cbc2.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2021-03-02更新
|
5407次组卷
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11卷引用:第一章 空间向量与立体几何单元检测(能力挑战卷)-【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)
(已下线)第一章 空间向量与立体几何单元检测(能力挑战卷)-【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)湖北省郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中等五校2022-2023学年高二上学期11月联考数学试题湖北省武汉市第三中学2022-2023学年高二上学期期中模拟数学试题湖北省五校2022-2023学年高二上学期11月联考数学试题(已下线)难关必刷01 空间向量的综合应用-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)浙江省宁波市宁海中学创新班2021届高三下学期2月测试数学试题(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)(已下线)专题1.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线) 专题20 立体几何角的计算问题(练)-2021年高三数学二轮复习讲练测(新高考版)(已下线)专题24 立体几何角的计算问题(练)-2021年高三数学二轮复习讲练测(文理通用)(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-3
2 . 如图,在四棱台ABCD-A1B1C1D1中,底面ABCD是菱形,∠ABC=
,∠B1BD=
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
您最近一年使用:0次
2020-03-19更新
|
5188次组卷
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10卷引用:安徽省合肥一中2020-2021学年高二上学期10月段考数学(理)试题
安徽省合肥一中2020-2021学年高二上学期10月段考数学(理)试题湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题广东省中山市2023-2024学年高二上学期期末统一考试数学试题2020届浙江省名校协作体高三下学期3月第二次联考数学试题山东省齐鲁2021-2022学年3月份高一阶段性质量检测试卷A福建省福州格致中学2022届高三数学模拟试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-22024年全国普通高中九省联考仿真模拟数学试题(三)湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题
3 . 如图,在三棱台
中,
,
,
为
的中点,二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/27d9a8c0-8a90-41b9-b258-50a946d9d5e0.png?resizew=189)
(1)证明:
;
(2)当
为何值时,直线
与平面
所成角的正弦值为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c01138acca46627f2dc26aeb95b4da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecca74150d296707924bad9ce67be9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/27d9a8c0-8a90-41b9-b258-50a946d9d5e0.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf21399dcf3682bf5d3f9cbd5eed86c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
您最近一年使用:0次
2020-01-05更新
|
3651次组卷
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4卷引用:【新东方】杭州高二数学试卷237
(已下线)【新东方】杭州高二数学试卷237湖北省武汉外国语学校2020-2021学年高一下学期期末数学试题河南省南阳市第一中学校2023-2024学年高三上学期开学考试数学试题(已下线)专题15 立体几何解答题全归类(9大核心考点)(讲义)-2
名校
4 . 如图,在梯形
中,
,
,
,现将
沿
翻折成直二面角
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/381bc715-77fe-4609-938a-ada15fa13cc5.png?resizew=468)
(Ⅰ)证明:
;
(Ⅱ)若异面直线
与
所成角的余弦值为
,求二面角
余弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de3595bb7c79503fabd75d99196ccb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbced129627233661d88e9663a9e13c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/381bc715-77fe-4609-938a-ada15fa13cc5.png?resizew=468)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82279b14a119057fdd78b85d63e669.png)
(Ⅱ)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
您最近一年使用:0次
2019-01-22更新
|
3814次组卷
|
4卷引用:江西省赣县第三中学2020-2021学年高二12月月考数学(理)试题
名校
5 . 如图1,在△
中,
,
分别为
,
的中点,
为
的中点,
,
.将△
沿
折起到△
的位置,使得平面
平面
,如图2.
![](https://img.xkw.com/dksih/QBM/2018/4/10/1921286677610496/1924179729383424/STEM/e517abdb-2d50-422b-b5da-90a750360645.png?resizew=431)
(1)求证:
;
(2)求直线
和平面
所成角的正弦值;
(3)线段
上是否存在点
,使得直线
和
所成角的余弦值为
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0117046e7a37bebe0c7b987a00d2bcb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://img.xkw.com/dksih/QBM/2018/4/10/1921286677610496/1924179729383424/STEM/e517abdb-2d50-422b-b5da-90a750360645.png?resizew=431)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e51c4114e94bceb198403c1858b9682.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c741af321a8ddaf387fa661f3920ad84.png)
您最近一年使用:0次
2018-04-14更新
|
5271次组卷
|
9卷引用:北京市第五十七中学2021-2022学年高二10月月考数学试题
北京市第五十七中学2021-2022学年高二10月月考数学试题重庆市实验中学校2021-2022学年高二上学期10月月考数学试题湖南省衡阳市祁东县育贤中学2022-2023学年高二上学期第一次月考数学试题北京市第一七一中学2023-2024学年高二上学期12月月考数学试题(已下线)难关必刷01 空间向量的综合应用-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)第一章 空间向量与立体几何(压轴题专练,精选20题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)单元高难问题01探索性问题(各大名校30题专项训练)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)北京市城六区2018届高三一模理科数学解答题分类汇编之立体几何北京市2019届高三数学理一轮复习典型题专项训练:立体几何