1 . 如图,已知正方体
的棱长为2,
,
分别是棱
,
的中点,点
为底面
内(包括边界)的动点,则以下叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.过![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.若直线![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
2 . 如图,在棱长为2的正方体
中,
为
内的任意一点(含边界),则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6701e148-7d5c-4f92-b9ad-cc4599b43a70.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de60f6ffd5ab327d4cfe32d26d95da70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/6701e148-7d5c-4f92-b9ad-cc4599b43a70.png?resizew=165)
A.三棱锥![]() |
B.点![]() ![]() ![]() |
C.向量![]() ![]() ![]() |
D.若线段![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 如图,在棱长为2的正方体
中,点
在平面
内且
,延长
交平面
于点
,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849b7c1951eb016e65f615d1a782af10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/46841383-a72a-41ab-aa77-f7a3095680fd.png?resizew=164)
A.线段![]() ![]() |
B.点![]() ![]() |
C.直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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解题方法
4 . 如图,已知直圆柱的上、下底面圆心分别为
,
是圆柱的轴截面,正方形
内接于下底面圆
,点
是
中点,
.
平面
;
(2)若点
为线段
上的动点,求直线
与平面
所成角的余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b464808cf5267a09ef7c593bd10af25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010fc88cbf6f12d72922cb9ef38756a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-10-11更新
|
1037次组卷
|
2卷引用:广西三新学术联盟2023-2024学年高二上学期10月联考数学试题
5 . 在直三棱柱
中,
,且
,
为线段
的中点,
为棱
上的动点,平面
过
三点,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b3abffbc8bfdd701f88b23e05e5306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62227b4b9cc501bee165642e9a3d5334.png)
A.三棱锥![]() |
B.平面![]() |
C.当![]() ![]() ![]() ![]() |
D.存在点![]() ![]() ![]() |
您最近一年使用:0次
2023-09-27更新
|
674次组卷
|
4卷引用:广西玉林市北流市实验中学等四校2023-2024学年高二上学期期中联考质量评价检测数学试题
广西玉林市北流市实验中学等四校2023-2024学年高二上学期期中联考质量评价检测数学试题辽宁省部分名校2023-2024学年高二上学期联考数学试题(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)广东省南粤名校2024届高三上学期9月学科综合素养评价联考数学试题
名校
6 . 如图,四棱锥
内,
平面
,四边形
为正方形,
,
.过
的直线
交平面
于正方形
内的点
,且满足平面
平面
.
(1)求点
的轨迹长度;
(2)当二面角
的余弦值为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd051fedb6691e2183e658f1fe487ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392469b357b12b998528499929366c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/1/1459c43b-c75d-4ea6-bb40-a3441af6132b.png?resizew=130)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1a4b8e6a3514ac93b69042d1f9553b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5c3c0ab9b7ba915604ed7e4e19254f.png)
您最近一年使用:0次
名校
解题方法
7 . 在
中,
,
分别是
上的点,满足
且
经过
的重心,将
沿
折起到
的位置,使
,
是
的中点,如图所示.
(1)求
与平面
所成角的大小;
(2)在线段
上是否存在点
(
不与端点
重合),使平面
与平面
垂直?若存在,求出
与
的比值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9453c18e40f13c75f430e2286f91e6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cae7cc6665dc8edfb9060075b3afb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a078495ba47076ccaa28b46f765d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2fef4031c10abc18c8747af6b9a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/23/9c9c456d-2e39-4975-bf92-618d717b249f.png?resizew=268)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b3c60399065a6979ef25c46f7ec949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d4248d9672aa3436ea1d9f1e267edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a604466a9c8d10d557b3dfc43b547065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
2023-09-18更新
|
1238次组卷
|
13卷引用:广西玉林市北流市实验中学等四校2023-2024学年高二上学期期中联考质量评价检测数学试题
广西玉林市北流市实验中学等四校2023-2024学年高二上学期期中联考质量评价检测数学试题江苏省常州市八校2021-2022学年高二下学期期中联考数学试题(已下线)高二上学期期中【夯实基础60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)四川省广安第二中学校2023-2024学年高二上学期第一次月考数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(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)2023-2024学年高二上学期数学期末预测能力卷(人教A版2019)(已下线)专题01 空间向量与立体几何(3)(已下线)第3章 空间向量及其应用(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)云南省昆明市第十中学2023届高三数学省测数学纠错试题云南省曲靖市麒麟区第一中学2023届高三下学期2月月考数学试题云南省昆明市寻甸回族彝族自治县民族中学2023届高三下学期2月月考数学试题云南省曲靖市宣威市第七中学2023届高三高考数学学情检测数学试题(一)
名校
解题方法
8 . 在正四面体
(所有棱长均相等的三棱锥)中,点
在棱
上,满足
,点
为线段
上的动点.设直线
与平面
所成的角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.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/a02c25b95e61557eec096de150ab873f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac93e58e9bba899df62a4cda5f1a5ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.存在某个位置,使得![]() | B.存在某个位置,使得![]() |
C.存在某个位置,使得平面![]() ![]() | D.存在某个位置,使得![]() |
您最近一年使用:0次
2020-07-16更新
|
1471次组卷
|
7卷引用:广西玉林市田家炳中学2020-2021学年高二上学期质量检测数学试题
广西玉林市田家炳中学2020-2021学年高二上学期质量检测数学试题(已下线)专题06 空间向量与立体几何(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)专题03 空间向量与立体几何的压轴题(一)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)浙江省杭州东方中学2022-2023学年高二上学期期中数学试题(已下线)第3章 空间向量及其应用 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)浙江省舟山中学2020届高三下学期6月高考仿真模拟数学试题(已下线)专题8-4 立体几何中求角度、距离类型-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
名校
9 . 如图所示的几何体
中,
和
均为以
为直角顶点的等腰直角三角形,
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/5/26/2471193277857792/2471708998156288/STEM/671926a565504cf289445e9b734199ea.png?resizew=237)
(1)求证:
;
(2)求二面角
的大小;
(3)设
为线段
上的动点,使得平面
平面
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be89b9d1709d7974a108142c5fa2ccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099dd87a526391f830ac2a11e7d7ad56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bbb16f9380dd62d556480a3944be31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66418ef39d3081d89411a4907d8599f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdf241efcd0c8026d188fad5a5ba4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2020/5/26/2471193277857792/2471708998156288/STEM/671926a565504cf289445e9b734199ea.png?resizew=237)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5ffe436f8eb53a211abf95baed8ca9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd548dfcef01e147e4dce25bd384f9b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0cf60b84dcb4baf97c39fe659e08a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910043595f4eed0c5b2a2246bec3664c.png)
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2020-05-27更新
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2399次组卷
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16卷引用:广西玉林市博白县第四中学(博白县中学书香校区)2022-2023学年上学期高二9月月考数学试题
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10 . 在四棱锥
中,平面
平面
,
为等边三角形,
,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/f1f9fdb1-7d4d-43a6-9769-373ae2e7ad05.png?resizew=226)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](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/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c313dff515240bc75d42f6687ac44cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/f1f9fdb1-7d4d-43a6-9769-373ae2e7ad05.png?resizew=226)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8d90d123fec1ae1b7b30dac9f88e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
您最近一年使用:0次
2020-02-09更新
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868次组卷
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6卷引用:广西壮族自治区南宁市兴宁区第三中学2019-2020学年高二上学期期末数学(理)试题