1 . 已知正方体
的棱长为
,
分别是棱
的中点,点
为底面
内(包括边界)的一动点,若直线
与平面
无公共点,则点
的轨迹长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a438de4d260b84dfde7d0fd492b9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/dcd0805d-e56c-40ab-b8ea-84c5a5fe7f56.png?resizew=180)
您最近一年使用:0次
名校
解题方法
2 . 如图,在棱长为1的正方体
中,点M是AD的中点,动点P在底面ABCD内(不包括边界),若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
平面
,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/dd3cfdde-afb4-4b89-bbc2-a6f083e04f88.png?resizew=142)
您最近一年使用:0次
2022-11-22更新
|
216次组卷
|
3卷引用:江西省宜春市第一中学2022-2023学年高二上学期期末考试数学试题
解题方法
3 . 如图,在边长为2的正方体
中,E,F,O分别为正方形
,
,ABCD的中心,点P在正方形ABCD内(含边界)运动,若直线
与平面DEF无交点,则点P所形成的轨迹___ 点O(填“经过”或“不经过”);该轨迹长度为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/cc2b6ba7-b76d-4874-9f55-349f8d5a03ff.png?resizew=212)
您最近一年使用:0次
名校
解题方法
4 . 如图,在正方体
中,E是线段
上的动点,下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/4ead815c-884c-4204-ae02-ea6ae784984b.png?resizew=164)
①
面
;
②
面
;
③二面角
的平面角为
;
④三棱锥
的体积不变.
其中正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/4ead815c-884c-4204-ae02-ea6ae784984b.png?resizew=164)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850305485a6d3ee30fe313dc8bb736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc741de0ca651a0f3ef1974c3bb52bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a91c2d02c8116e99111c488056553d.png)
其中正确结论的序号为
您最近一年使用:0次
2022-01-25更新
|
228次组卷
|
2卷引用:四川省眉山市2021-2022学年高二上学期期末数学(文)试题
名校
解题方法
5 . 如图,在长方体
中,
,
,
,
分别是
,
的中点,则下列四个结论中成立的是________ .(写出对应的序号)
①
平面
;
②
;
③
;
④长方体
的外接球表面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d150134e5018f74fc4e8a016ced5f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b027ebfa72e944eeebd9c1298b9a17a.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/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9480c44a25280485a814210df4e5801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc01e615163441c39b330ad4680b5c1a.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1ad2345fb1feffd7b8d34a78805bc2.png)
④长方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9dccf5e8a34c10d6266dc6691240920.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/4eec410d-e03d-44fd-9fe6-d66832f5a3ec.png?resizew=144)
您最近一年使用:0次
2021-05-30更新
|
608次组卷
|
7卷引用:新疆克拉玛依市第一中学2020-2021学年高二下学期期末数学试题
新疆克拉玛依市第一中学2020-2021学年高二下学期期末数学试题安徽省合肥市长丰县衡安学校2020-2021学年高二下学期第四次调研考试文科数学试题陕西省2021届高三下学期教学质量检测测评(五)文科数学试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(乙卷)数学(文)试题(已下线)“超级全能生”2021届高三全国卷地区5月联考试题(甲卷)数学(文)试题(已下线)考点29 空间几何体的结构及其三视图与直观图-备战2022年高考数学(文)一轮复习考点帮(已下线)考向33 空间中的平行关系
名校
6 . 如图,在棱长为1的正方体ABCD-A1B1C1D1中,点E,F分别是棱BC、CC1的中点,
是侧面BCC1B1内一点(含边界),若A1P
平面AEF,点P的轨迹长度为___________ .直线A1P与平面BCC1B1所成角的正切值的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645166353424384/2645303562756096/STEM/dba19e47-a059-46de-82bf-386e9d695a03.png?resizew=212)
您最近一年使用:0次
7 . 如图,正方体
的棱长为
,
分别为
的中点,
是底面
上一点.若
平面
,则
长度的最小值是___ ;最大值是___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921321d7e2270868fa847d1e69aab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d8677ae5ca7acf874d93789425d172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/2021/1/23/2641918816354304/2642886913941504/STEM/7ea14152-d49e-4944-8cc9-759065c47a81.png)
您最近一年使用:0次
2021-01-24更新
|
1535次组卷
|
6卷引用:北京市西城区2020-2021学年高二上学期期末考试数学试题
北京市西城区2020-2021学年高二上学期期末考试数学试题江苏省南京市第一中学2022-2023学年高二下学期期末数学试题北京市第六十六中学2023-2024学年高二上学期第一次质量检测数学试题北京市朝阳区东北师范大学附属中学朝阳学校2023-2024学年高二上学期期中学习质量监测与反馈数学试卷(已下线)专题8.4 空间直线、平面的平行(B卷提升篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版,浙江专用)(已下线)第一章 点线面位置关系 专题一 空间平行关系的判定与证明 微点2 空间平行关系的判定与证明综合训练【培优版】
解题方法
8 . 在正方体
中,
是棱
的中点,点
在棱
上,若
平面
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb0e486515172bbc2b10956de1001c8.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f845e74c18cdb2d6a80e0c0b4e85cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912d03b664bbf5896427da55c5d4e0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb0e486515172bbc2b10956de1001c8.png)
您最近一年使用:0次
9 . 在棱长为
的正方体
中,
是棱
的中点,
是侧面
内的动点,且
平面
,则点
形成的轨迹的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094e639c2b31dc54b1b3e6456e77843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dd27701a0a9849b58d39ae10623763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de70dbffc7d55126e47be65632b459a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6ffadcdc4aa377012f3b9de8436e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
10 . 点
分别是正方体
的棱
的中点,如图所示,则下列命题中的真命题是________ (写出所有真命题的编号).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/11d8c9e4-391c-45dd-8e14-86e13023c078.png?resizew=173)
①以正方体的顶点为顶点的三棱锥的四个面中最多只有三个面是直角三角形;②点
在直线
上运动时,总有
;③点
在直线
上运动时,三棱锥
的体积的定值;④若点
是正方体的面
内的一动点,且
到点
和
距离相等,则点
的轨迹是一条线段.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c526cb5d2242b7536f4620bd816bd2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/11d8c9e4-391c-45dd-8e14-86e13023c078.png?resizew=173)
①以正方体的顶点为顶点的三棱锥的四个面中最多只有三个面是直角三角形;②点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e32cf73c01995c91c3523fa11b3bd7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8b73e5f21858fd4caabf9c086d0bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次