1 . 正三棱柱
的底面边长是4,侧棱长是6,
,
分别为
,
的中点,若
是侧面
上一点,且
平面
,则线段
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc674d2604ff270dd6abc66b35e86e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
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解题方法
2 . 已知
为
所在平面外一点,
是
中点,
是
上一点.若
平面
,则
的值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1ef332e81b9dbaf0075a345711b02c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55031fef94c6b47c0f63261f84a4d37d.png)
您最近一年使用:0次
解题方法
3 . 如图,棱长为2的正方体
中,
,
分别是线段
和
上的动点.对于下列四个结论:
①存在无数条直线
平面
;
②线段
长度的取值范围是
;
③三棱锥
的体积最大值为
;
④设
,
分别为线段
和
上的中点,则线段
的垂直平分线与底面的交点构成的集合是圆.
则其中正确的命题有______ .
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/48fb23f6-6b8b-4ba1-8ddf-90ee23535b48.png?resizew=161)
①存在无数条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab03deb15e25f16f9bae24d5aac4e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
②线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599f32abea48b3914142615dbc9e2613.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d492a2248463e0c0199a25d0f76d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
则其中正确的命题有
您最近一年使用:0次
解题方法
4 . 如图,在正方体
中,
为棱
的中点,
为棱
(含端点)上的一个动点.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/6d6492fd-1498-49e7-aee0-3af641590d0d.png?resizew=165)
①存在符合条件的点
,使得
平面
;
②不存在符合条件的点
,使得
;
③异面直线
与
所成角的余弦值为
;
④三棱锥
的体积的取值范围是
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6293a2528570eda7fef7c784efc7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/6d6492fd-1498-49e7-aee0-3af641590d0d.png?resizew=165)
①存在符合条件的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9f260496ba23993238601a89eca5c.png)
②不存在符合条件的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a3dc3f3a02f4400e22dec2f2fee23.png)
③异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becf2941e15d668d93ea6ed980afd0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cd8ecd9806e3a8c9b2de96110970b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31458a4ee26d560cf1f3e438f5b602.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
5 . 如图, 在圆台
中,
,点C是底面圆周上异于A、B的一点,
, 点D是
的中点,
为平面
与平面
的交线, 则交线
与平面
所成角的大小为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb81f6270ed053e3f8e88da65865af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8406f2441769ce49264ccca6585dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a8735eaaaa942e757f1bf9d84d0c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c643d1581b072f4b61a2211828eb0569.png)
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2024-01-29更新
|
618次组卷
|
6卷引用:广东省深圳市高级中学2023-2024学年高三上学期第三次诊断测试数学试题
广东省深圳市高级中学2023-2024学年高三上学期第三次诊断测试数学试题(已下线)重难点6-1 空间角与空间距离的求解(8题型+满分技巧+限时检测)(已下线)第13讲 8.6.2直线与平面垂直的性质定理 (第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)高一下学期期中复习填空题压轴题十七大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)
名校
解题方法
6 . 已知
表示三个不同的平面,若
,且
,则直线
,
的位置关系是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f747152f006301e03b643afb80195c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea0bb5989b28576a3a574b3c9e96ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2024-01-19更新
|
522次组卷
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5卷引用:上海市闵行(文琦)中学2023-2024学年高二上学期期末考试数学试题
上海市闵行(文琦)中学2023-2024学年高二上学期期末考试数学试题(已下线)第05讲 空间直线﹑平面的平行-《知识解读·题型专练》(已下线)8.5.3 平面与平面平行【第一练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)6.4.2平面与平面平行-【帮课堂】(北师大版2019必修第二册)专题05 空间直线与平面-《期末真题分类汇编》(上海专用)
名校
7 . 如图所示,在棱长为1的正方体
中,设
分别是线段
、
上的动点,若
平面
,则线段
长的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad57e3727b7bbd795b05332fbf9649e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2024-01-19更新
|
823次组卷
|
8卷引用:上海市上海交通大学附属中学2023-2024学年高二上学期期末考试数学试卷
上海市上海交通大学附属中学2023-2024学年高二上学期期末考试数学试卷(已下线)8.5.1直线与平面平行(已下线)8.5.2 直线与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路湖南省慈利县第一中学2023-2024学年高一下学期期中考试数学试题(已下线)6.4.1直线与平面平行-【帮课堂】(北师大版2019必修第二册)(已下线)11.3.2直线与平面平行-同步精品课堂(人教B版2019必修第四册)广东省湛江市第二十一中学2023-2024学年高一下学期期中考试数学试卷(已下线)期末测试卷03-《期末真题分类汇编》(上海专用)
名校
解题方法
8 . 如图,棱长为2的正方体
中,点P在线段
上运动,以下四个命题:①三棱锥
的体积为定值;②
;③若
平面ABCD,则三棱锥
的外接球半径为
;④
的最小值为
.其中真命题有______ (写出所有真命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a80afb14665ad9cb3587c5364980e30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763be97fe1e030b5509bda231a546001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae737bd4c7f31bdc93155459a48d8457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8571fe486121ccf36f6be04dbb2295c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e102741bc350e8ccbc6d1405b44972d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed728f911042364c77b78b597aafd344.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/5/b2614923-7e0e-4636-80c2-c49ca6630749.png?resizew=160)
您最近一年使用:0次
9 . 已知m、n是不重合的直线,
和
是不重合的平面,有下列命题:
(1)若
,
,则
; (2)若
,
,则
;
(3)若
,
,则
且
; (4)若
,
,则
,
其中真命题的个数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0d37b44de48de51555fa95d94e33f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80645381feb9746cc149da61d553974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384a65ca1ee3d7d86b988ca34c885e18.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3bdd7a1a12d66a8b32e239fd6886a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80645381feb9746cc149da61d553974a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c6d37467a5c995d71e49408503927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe920cd78db25f5b4df37d066e57800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b610e3c5b3d78a5730e7f3d736ac28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384a65ca1ee3d7d86b988ca34c885e18.png)
其中真命题的个数是
您最近一年使用:0次
名校
解题方法
10 . 如图,在正四棱柱
中,底面
是正方形,且
,
,经过顶点A和
各作一个平面与平面
平行,前者与平面
交于
,后者与平面
交于
,则异面直线
与
所成角的余弦值为______ .
![](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/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
您最近一年使用:0次
2024-01-11更新
|
549次组卷
|
6卷引用:上海市徐汇区2023-2024学年高二上学期期末统考数学试卷
上海市徐汇区2023-2024学年高二上学期期末统考数学试卷(已下线)第11讲 8.6.1 直线与直线垂直-【帮课堂】(人教A版2019必修第二册)(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(1)-单元速记·巧练(人教A版2019必修第二册)北京市第八十中学2023-2024学年高一下学期期中考试数学试题专题05 空间直线与平面-《期末真题分类汇编》(上海专用)