1 . 如图,在四棱锥
中,
平面
,
为
中点,点
在梭
上(不包括端点).
平面
;
(2)若点
为
的中点,求直线
到平面
的距离.
![](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/6c87a0b2558b7890f0d5cacc6c09f7a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885592836e5cb6c2df440fc039c696a4.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-04-13更新
|
2201次组卷
|
6卷引用:宁夏回族自治区银川一中2024届高三第三次模拟考试理科数学试题
宁夏回族自治区银川一中2024届高三第三次模拟考试理科数学试题吉林省吉林地区普通高中2024届高三第三次模拟考试数学试题(已下线)模块五 专题3 全真能力模拟3(苏教版高二期中研习)(已下线)第33题 空间距离解法笃定,向量方法建系第一(优质好题一题多解)(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数学试题
名校
解题方法
2 . 如图,在四棱锥
中,底面
是正方形,
底面
,
,点
是棱
的中点,点
是棱
上靠近点
的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/985b6ced-f940-44e0-866d-9e59c5724e3f.png?resizew=153)
(1)证明:
;
(2)求点
到平面
的距离.
![](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/7c656a1d0532dd79ef1e61c807b7f6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/985b6ced-f940-44e0-866d-9e59c5724e3f.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac559a1a89bfb16e1c44cdd7ad2f2bbd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2023-12-02更新
|
281次组卷
|
6卷引用:宁夏银川市唐徕中学2023-2024学年高二上学期第一次月考数学试题
3 . 在空间直角坐标系中,三棱锥
,
,
,
.
(1)求三棱锥
的体积
(2)用求轨迹方程的思想方法,试求在空间直角坐标系中,以
为方向向量,过点
的直线方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44d99c49033e54fd2c09b45433f9af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa890092a50602193f635d2d20d4464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c567f847a7835865cb037c14034ff.png)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)用求轨迹方程的思想方法,试求在空间直角坐标系中,以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44d99c49033e54fd2c09b45433f9af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789a325242b32beee8b82f934f4177f0.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在长方体
中,
,E为线段
的中点,F为线段
的中点.
(1)求直线
到直线AE的距离;
(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/364a80d9f06234699e14b6117211563c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/812476d9-47df-4235-b0ca-74b5b515d894.png?resizew=130)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2023-09-18更新
|
748次组卷
|
5卷引用:宁夏银川市永宁县上游高级中学2023-2024学年高二上学期月考(一)数学试题
宁夏银川市永宁县上游高级中学2023-2024学年高二上学期月考(一)数学试题(已下线)高二上学期期中复习【第一章 空间向量与立体几何】十大题型归纳(拔尖篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)福建省厦门海沧实验中学2023-2024学年高二上学期10月阶段性检测数学试题(已下线)模块一 专题1 空间向量与立体几何(人教A)2(已下线)高二上期中真题精选(压轴60题30个考点专练)【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)
名校
解题方法
5 . 如图,在直三棱柱
中,
,点
是线段
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/852c95ae-28ba-415a-a786-465d50bcaadf.png?resizew=149)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)求
点到平面
的距离;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a24f98e506cdd4b705004924b8759b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/852c95ae-28ba-415a-a786-465d50bcaadf.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
您最近一年使用:0次
2023-09-17更新
|
1842次组卷
|
9卷引用:宁夏回族自治区银川一中2023-2024学年高二上学期期中考试数学试题
宁夏回族自治区银川一中2023-2024学年高二上学期期中考试数学试题浙江省台州市八校联盟2022-2023学年高二上学期11月期中联考数学试题河北省保定市定州中学2023-2024学年高二上学期9月月考数学试题黑龙江省佳木斯市东风区第八中学2023-2024学年高二上学期10月月考数学试题(已下线)模块一 专题1 空间向量与立体几何(人教A)2(已下线)模块一 专题2 利用空间向量解决立体几何问题 (讲)1 期末终极研习室(2023-2024学年第一学期)高二人教A版江苏省江阴市第一中学2024届高三上学期12月阶段测试数学试题江苏省镇江市镇江第一中学2024届高三上学期12月阶段测试数学试题河南省漯河市实验高级中学2024届高三上学期1月阶段模拟测试数学试题
解题方法
6 . 在正四棱柱
中,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2023/1/18/3155699549495296/3158553189507072/STEM/65ef36b0118f4bb0b18fd5a7e60eda39.png?resizew=187)
(1)求直线
与平面
所成的角;
(2)求异面直线
与
所成的角;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fc166a6287ed378b99177440e21424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/2023/1/18/3155699549495296/3158553189507072/STEM/65ef36b0118f4bb0b18fd5a7e60eda39.png?resizew=187)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
您最近一年使用:0次
2023-01-22更新
|
198次组卷
|
7卷引用:宁夏贺兰县景博中学2019-2020学年高二上学期第二次月考数学(理)试题
宁夏贺兰县景博中学2019-2020学年高二上学期第二次月考数学(理)试题专题1.4 空间向量与立体几何(A卷基础篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)河北省唐山市遵化市2021-2022学年高二上学期期中数学试题湖南省怀化市湖天中学2022-2023学年高二上学期期中数学试题吉林省白城市洮南市第一中学2021-2022学年高二上学期第一次月考数学试题贵州省黔西南州金成实验学校2023-2024学年高二上学期期中考试数学试题(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【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)
名校
解题方法
7 . 如图,直角梯形
与等腰直角三角形
所在的平面互相垂直,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877066904535040/2877864959655936/STEM/1b2a2272-edfd-4a76-9e2c-00764de71c38.png?resizew=171)
(1)求点C到平面
的距离;
(2)线段
上是否存在点F,使
与平面
所成角正弦值为
,若存在,求出
,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53824871cc1e0995c339bc4fc00777a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbf6796681347c82b07c4dd30800f1a.png)
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877066904535040/2877864959655936/STEM/1b2a2272-edfd-4a76-9e2c-00764de71c38.png?resizew=171)
(1)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1569f8c3aca0b4a687df6792984a9cb.png)
您最近一年使用:0次
2021-12-22更新
|
593次组卷
|
3卷引用:宁夏银川一中2021-2022学年高二上学期期末考试数学(理)试题
8 . 如图,在四棱锥
中,侧面
底面
,侧棱
,
,底面
为直角梯形,其中
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/7/5/1572891139973120/1572891146084352/STEM/a2ea943dea1f4823a35dfbb8e139c8e6.png?resizew=186)
(1)求证:
平面
;
(2)求
点到平面
的距离;
(3)线段
上是否存在一点
,使得二面角
的余弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2016/7/5/1572891139973120/1572891146084352/STEM/a2ea943dea1f4823a35dfbb8e139c8e6.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)线段
![](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/9f8b47a0a7c3029a7c7ed3ed5b4993fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff82dc4f9daf2658ee50f550ffdeac58.png)
您最近一年使用:0次
12-13高二上·宁夏银川·期末
9 . 如图,
平面
,四边形
是正方形,
,点
、
、
分别为线段
、
、
的中点.在线段
上是否存在一点
,使得点
到平面
的距离恰为
?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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.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)
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