名校
解题方法
1 . 如图,已知三棱柱
的侧棱与底面垂直,
,
,M,N分别是
,
的中点,点
在线段
上,且
.
;
(2)当
取何值时,直线
与平面
所成角
最小?
(3)是否存在点
,使得平面
与平面
所成的二面角的正弦值为
,若存在,试确定点
的位置,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597362da92c667625827a89c1c2e3dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ece75fe9b8555909be5a00d2b7af0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c29c3bfdae2d4fbe8a8deaa572a2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-06-09更新
|
352次组卷
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2卷引用:江苏省淮安市洪泽中学,金湖中学,清河中学,清浦中学等学校2023-2024学年高二下学期5月月考数学试题
名校
解题方法
2 . 在四棱锥
中,底面
是边长为3的正方形,
底面
,点
在侧棱
上,且满足
,则异面直线
和
的距离为( )
![](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/f7992a6b8d2458fca5dbe44c4320e9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda041848f97502ffc755f1ce484f92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-08更新
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486次组卷
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4卷引用:江苏省淮安市洪泽中学,金湖中学,清河中学,清浦中学等学校2023-2024学年高二下学期5月月考数学试题
江苏省淮安市洪泽中学,金湖中学,清河中学,清浦中学等学校2023-2024学年高二下学期5月月考数学试题江苏省靖江高级中学2023-2024学年高二下学期期中考试数学试题甘肃省兰州第一中学2023-2024学年高二下学期5月月考数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)
名校
解题方法
3 . 如图,圆锥是由直角
旋转而成,母线
,底面圆的半径为1,D是AB的中点,
为底面圆上的一点且
,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/0911f719-761e-4d07-bb6b-7495a6ac73b1.png?resizew=138)
(1)求点
到平面ABC的距离;
(2)求直线CD与平面AOB所成的角的正弦值;
(3)求点O到直线CD的距离,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56387ff53874620addcb0b91a605a309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6dd90426fd49c73816c14e4a56ab85e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/0911f719-761e-4d07-bb6b-7495a6ac73b1.png?resizew=138)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)求直线CD与平面AOB所成的角的正弦值;
(3)求点O到直线CD的距离,
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2024-04-08更新
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2卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
解题方法
4 . 将边长为2的正方形ABCD沿对角线AC折叠使得△ACD垂直于底面ABC,则异面直线AD与BC的距离为______ .
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2卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
5 . 2023年12月19日至20日,中央农村工作会议在北京召开,习近平主席对“三农”工作作出指示.某地区为响应习近平主席的号召,积极发展特色农业,建设蔬菜大棚.如图所示的七面体
是一个放置在地面上的蔬菜大棚钢架,四边形ABCD是矩形,
m,
m,
m,且ED,CF都垂直于平面ABCD,
m,
,平面
平面ABCD.
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09030a47bf268b6ea0c341ca76c2358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8fe3b14007e4be4c99c85e5b9610a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d824078abdd94782c09ccc39ddb539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17980426cd9d489706fdc45b81b9f92.png)
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
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4卷引用:江苏省淮安市金湖中学,清江中学,涟水郑梁梅高级中学等2023-2024学年高二下学期4月期中数学试题
名校
解题方法
6 . 在正方体
中,
,点P满足
,其中
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9dd1458186cfbdf0701ba835572721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
7 . 正四面体的棱长为
,点M为平面
内的动点,且满足
,则直线PM与直线AB的所成角的余弦值的取值范围为
您最近一年使用:0次
名校
8 . 如图,在斜三棱柱
中,
是边长为2的正三角形,
是以AC为斜边的等腰直角三角形且侧面
底面
,点
为
中点,点
为
的中点.
平面
;
(2)求平面
与平面
夹角的正弦值.
(3)过
作与
垂直的平面
,交直线
于点
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a715009a5804dc935ade37f5ac51591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
您最近一年使用:0次
2024-04-01更新
|
455次组卷
|
3卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
解题方法
9 . 设三个向量
不共面,那么对任意一个空间向量
,存在唯一的有序实数组
,使得:
成立.我们把
叫做基底,把有序实数组
叫做基底
下向量
的斜坐标.已知三棱锥
.以
为坐标原点,以
为
轴正方向,以
为y轴正方向,以
为
轴正方向,以
同方向上的单位向量
为基底,建立斜坐标系,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb4f795474089c4ca5183f0b8c8210d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977e7b03370104a3b2a99d7b2fc207e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f263fe996c25f0e231e27d2be0262275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82421141d6bb7a2f079659984133fe23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6592338e3a40aeb3f59f6817aad98899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d6c690993b231b20c7a969178e5c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7972794bf959560d01203713beeb5b08.png)
A.![]() | B.![]() ![]() |
C.若![]() ![]() | D.异面直线AP与BC所成角的余弦值为![]() |
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2024-04-01更新
|
181次组卷
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3卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
10 . 如图1,已知
是直角梯形,
,
,
,C、D分别为BF、AE的中点,
,
,将直角梯形
沿
翻折,使得二面角
的大小为
,如图2所示,设N为
的中点.
;
(2)若M为AE上一点,且
,则当
为何值时,直线BM与平面ADE所成角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25eff69a4a0dc7a7ab183843303d333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f0bc01c1dbf0b4b87763141d8059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085b59baa6aaeab11a2efda83603724b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bfc65bfbc357d43069e9aad18f8625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdadcc147a7e441decf7561c9e7310e.png)
(2)若M为AE上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668c259a8971e91fcc2867bed20ca3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d172f55bc57ef5b5c2c1ad5b167440b2.png)
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2024-03-25更新
|
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4卷引用:江苏省洪泽中学等七校2023-2024学年高二下学期第一次联考数学试卷
江苏省洪泽中学等七校2023-2024学年高二下学期第一次联考数学试卷河南省信阳高级中学2023-2024学年高二下学期4月测试(一)数学试题(已下线)模块4 二模重组卷 第2套 复盘卷(已下线)专题01 空间向量与立体几何解答题必考题型(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)