名校
解题方法
1 . 如图所示,在棱长为2的正方体
中,E,F,G分别为所在棱的中点,P为平面
内(包括边界)一动点,且
∥平面EFG,则P点的轨迹长度为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a80427c5520818aa57e4de7bb5ce7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
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2023-07-23更新
|
853次组卷
|
5卷引用:福建省福州屏东中学2022-2023学年高一下学期期末考试数学试题
福建省福州屏东中学2022-2023学年高一下学期期末考试数学试题江西省乐安县第二中学2023-2024学年高二上学期入学检测数学试题(已下线)专题突破卷21 立体几何的轨迹问题(已下线)重难点突破04 立体几何中的轨迹问题(六大题型)(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)
2 . 如图,在正四棱柱
中,四边形
是边长为2的正方形,
分别是棱
的中点,
分别是棱
上动点.当直线
与底面
所成角最小时线段
的长度是__________ ,四面体
的体积是__________ .
![](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/cc814fa51a659b3eb6b11ab4770df0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46c696ff5f123a482bae81cf9a1b570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570661f3cd27119447394748b3bae6bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cfd0530c5623a89ec6a6652a367e2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/264bcff6-4d98-4a29-95dc-bf7e77eb8a9d.png?resizew=135)
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,E是棱
的中点,O是BE的中点,过点О作平面
的垂线,交平面
于点F,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65984d934d0f6ba7e709b86034dcc2c.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6668c79fb70d1fef682cdf629a851ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65984d934d0f6ba7e709b86034dcc2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/62dd6a23-9964-42d5-a839-ec9bc82f103a.png?resizew=164)
您最近一年使用:0次
解题方法
4 . 在长方体
中,
,
,E,F,G分别是棱AB,BC,
的中点,P是底面ABCD内一动点,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
平面EFG,当BP最短时,三棱锥
外接球的体积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3829997d8af2e692f030cb359761f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16384e20db8a965fa73fc2d9f48a4017.png)
您最近一年使用:0次
2022-07-18更新
|
835次组卷
|
2卷引用:福建省永泰县第一中学2022-2023学年高二上学期开学考试数学试题
解题方法
5 . 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
6 .
分别为菱形
的边
的中点,将菱形沿对角线
折起,使点
不在平面
内,则在翻折过程中,以下命题正确的是___________ .(写出所有正确命题的序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/24920187-fda8-4296-a57d-2223a05f1d9d.png?resizew=319)
①
平面
;②异面直线
与
所成的角为定值;③在二面角
逐渐渐变小的过程中,三棱锥
的外接球半径先变小后变大;④若存在某个位程,使得直线
与直线
垂直,则
的取值范围是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/24920187-fda8-4296-a57d-2223a05f1d9d.png?resizew=319)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
您最近一年使用:0次
2020-03-15更新
|
1351次组卷
|
9卷引用:2020届福建省福州第一中学高三上学期期末考试数学(理)试题
2020届福建省福州第一中学高三上学期期末考试数学(理)试题(已下线)理科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》(已下线)文科数学-2020年高考押题预测卷03(新课标Ⅱ卷)《2020年高考押题预测卷》内蒙古赤峰二中2020-2021学年高二上学期第一次月考数学(理科)试题(已下线)专题8.8 立体几何综合问题(练)-2021年新高考数学一轮复习讲练测(已下线)专题8.8 立体几何综合问题(练)- 2022年高考数学一轮复习讲练测(新教材新高考)四川省内江市第六中学2022届高三下学期考前强化训练二数学(理科)试题四川省内江市第六中学2022届高三下学期考前强化训练二数学(文科)试题(已下线)专题06 立体几何(理)第二篇-备战2020高考数学黄金30题系列之压轴题(新课标版)
名校
7 . 在棱长为1的正方体
中,点
是对角线
上的动点(点
与
不重合),则下列结论正确的是__________
![](https://img.xkw.com/dksih/QBM/2019/12/12/2353628685033472/2356424106745856/STEM/d98b8dec128c4139ab9d7d07d2c074ad.png?resizew=189)
①存在点
,使得平面
平面
;
②存在点
,使得平面
平面
;
③
的面积可能等于
;
④若
分别是
在平面
与平面
的正投影的面积,则存在点
,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e484e13f1fb52adf6590e5a211c9bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c3246cc6148083e6f8f38d1aa2b318.png)
![](https://img.xkw.com/dksih/QBM/2019/12/12/2353628685033472/2356424106745856/STEM/d98b8dec128c4139ab9d7d07d2c074ad.png?resizew=189)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba49eb8ddd4dd38c1f994ccec93430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f3b7eb189fc65f5297c614cc0e3b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996bc28ce4aeea5c8959767d7d1fa80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769587deb84abb31c437b51f9a3be89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
您最近一年使用:0次
2019-12-16更新
|
829次组卷
|
7卷引用:福建省莆田市莆田第七中学2019-2020学年高三上学期期中数学(文)试题