名校
1 . 如图,已知正方体
的棱长为2,点E是
内(包括边界)的动点,则下列结论中正确的序号是________ (填所有正确结论的序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/7e11cc65-4391-4ccf-a3fb-a5d662976513.png?resizew=170)
①若
,
,则
平面
;
②若平面
与正方体各个面都相交,且
,则截面多边形的周长一定为
;
③若
的角平分线交AB于点F,且
,则动点E的轨迹长为
;
④直线
与平面
所成的角的余弦值的最大值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/7e11cc65-4391-4ccf-a3fb-a5d662976513.png?resizew=170)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f1d0b5e4a6ebf4405b98a21a1ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44edb46eb17d224e0d9a2667c2e5df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
②若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bc6a7e1ace458b04b99247bca0accd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a55a1a244f81097e05e715b69580faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f31a3724c639f88486f8356ca65397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06beac41f26a7735bbeff2e7df52f51d.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
您最近一年使用:0次
2023-04-25更新
|
443次组卷
|
2卷引用:四川省泸县第五中学2023届高考适应性考试数学(理)试题
2 . 已知三棱锥
的四个面都是边长为2的正三角形,
是
外接圆
上的一点,
为线段
上一点,
,
是球心为
,半径为
的球面上一点,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2e528bb8fc7c95fec7ecc510d04034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2226117019d1d41654fe6b36e14fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2023-03-26更新
|
547次组卷
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2卷引用:四川省宜宾市2023届高三下学期第二次诊断性测试理科数学试题
名校
解题方法
3 . 某儿童玩具的实物图如图1所示,从中抽象出的几何模型如图2所示,由
,
,
,
四条等长的线段组成,其结构特点是能使它任意抛至水平面后,总有一条线段所在的直线竖直向上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f32e63192e3b7dced9bf97aba128b6.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f32e63192e3b7dced9bf97aba128b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/4e4ff7f6-9423-4205-bd2b-25c4eebb5bd9.png?resizew=312)
您最近一年使用:0次
2023-02-08更新
|
1256次组卷
|
8卷引用:四川省成都市成都市第七中学2022-2023学年高一下学期期末数学试题
名校
解题方法
4 . 如图,在正方体
,中,E,F,G分别为棱
上的点(与正方体顶点不重合),过
作
平面
,垂足为H.设正方体
的棱长为1,给出以下四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/6aa4f3e3-05e3-4341-8711-c65e7f43d69a.png?resizew=172)
①若E,F,G分别是
的中点,则
;
②若E,F,G分别是
的中点,则用平行于平面
的平面去截正方体
,得到的截面图形一定是等边三角形;
③
可能为直角三角形;
④
.
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/244fad1219f5787edc48dc684f8fdc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d70675215ce4afa6a7d134fc073cd91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/6aa4f3e3-05e3-4341-8711-c65e7f43d69a.png?resizew=172)
①若E,F,G分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244fad1219f5787edc48dc684f8fdc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466e86468e42cd7904625a6ac336bb72.png)
②若E,F,G分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244fad1219f5787edc48dc684f8fdc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a9a1dff9f23589943575780dd580ce.png)
其中所有正确结论的序号是
您最近一年使用:0次
2022-05-17更新
|
1556次组卷
|
7卷引用:四川省宜宾市第四中学校2023届高考适应性考试数学(理)试题
四川省宜宾市第四中学校2023届高考适应性考试数学(理)试题北京市朝阳区2022届高三二模数学试题(已下线)考点7-2 三视图、截面与外接球 (文理)(已下线)考向26空间几何体的表面积与体积(重点)-2北京市第二中学2022-2023学年高二上学期10月学段考试数学试题北京市海淀区第五十七中学2022-2023学年高二上学期12月月考数学试题专题11空间中直线、平面的平行与垂直关系(选择填空题)
名校
解题方法
5 . 在棱长为
的正方体
中,
分别为
的中点,
为正方体棱上一动点.下列说法中所有正确的序号是___________
①
在
上运动时,存在某个位置,使得
与
所成角为
;
②
在
上运动时,
与
所成角的最大正弦值为
;
③
在
上运动且
时,过
三点的平面截正方体所得多边形的周长为
;
④
在
上运动时(
不与
重合),若点
在同一球面上,则该球表面积最大值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fee291a77b75c3bf7b2255b475211bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ae10933017e734cb333766920e4c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748952a03ee743295c7095917703d7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23552e1933f291d0a4c3f4d3b9371f5d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f1bf177e3452d43debfdd7f7d28ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e0166cef87d437ba03524bbdb61288.png)
您最近一年使用:0次
2022-04-08更新
|
1550次组卷
|
6卷引用:四川省达州市2022届高三第二次诊断性测试理科数学试题
四川省达州市2022届高三第二次诊断性测试理科数学试题甘肃省高台县第一中学2022届高三下学期第七次检测数学(文)试题(已下线)考向27 空间点、直线、平面之间的位置关系(重点)江西省南昌市第十中学2023届高三第一次模拟数学(文)试题江西省南昌市第十中学2023届年高三第一次模拟数学(理)试题(已下线)点线面之间的位置关系