名校
解题方法
1 . 如图,长方体
中,
,
分别为
中点,点P在平面
内,若直线
平面
,则线段
长度的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032f70b127f01219f3d90f8a5ae3a2b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572c2f57dce9bb7458f71d84f3c6a725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff55f4780bb3fb376c9a04dbfbb1d989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
您最近一年使用:0次
2021-07-24更新
|
768次组卷
|
16卷引用:2020届广西南宁市高三一模摸底数学(理科)试题
2020届广西南宁市高三一模摸底数学(理科)试题广西壮族自治区南宁市2019-2020学年高三上学期10月月考数学(理)试题广西壮族自治区南宁市2019-2020学年高三上学期10月月考数学(文)试题湖南省长沙市第一中学2019-2020学年高三下学期第八次月考理科数学试题湖南省长沙一中2020届高三(下)月考数学(理科)试题(八)河北正定中学2021届高三上学期第一次半月考试数学试题(已下线)【新东方】绍兴qw136上海市位育中学2020-2021学年高二下学期3月月考数学试题上海市进才中学2020-2021学年高二下学期期中数学试题广东省佛山市顺德区十一校联盟2020-2021学年高一下学期第二次段考数学试题上海市闵行中学2021-2022学年高二上学期10月月考数学试题上海市普陀区甘泉外国语中学2021-2022学年高二上学期期中数学试题上海市文来中学2021-2022学年高二上学期期中数学试题(已下线)8.5空间直线、平面的平行C卷安徽省六安市舒城中学2021-2022学年高一下学期期中数学试题(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(2)
名校
解题方法
2 . 在棱长为1的正方体
中,
是侧面
内一点(含边界)则下列命题中正确的是(把所有正确命题的序号填写在横线上)______ .
①使
的点
有且只有2个;
②满足
的点
的轨迹是一条线段;
③满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
平面
的点
有无穷多个;
④不存在点
使四面体
是鳖臑(四个面都是直角三角形的四面体).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e05241efa370017b863e6e0fe72bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
①使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7facb932529ae0d511d77714cf9e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac117747fb221b7f976577c5fb824084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
③满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
④不存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90671eb673c449b2b257ca23848f2f4c.png)
您最近一年使用:0次
2022-12-26更新
|
460次组卷
|
3卷引用:陕西省宝鸡市2023届高三上学期一模理科数学试题
名校
解题方法
3 . 在棱长为
的正方体
中,
是底面
内动点,且
平面
,当
最大时,三棱锥
的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57132b0bd38c035fec010ee3be1bc8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3103a9cf96b0cc54b301400c2d44b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c506d73df4b388ba073dfe8ad4e1c992.png)
您最近一年使用:0次
2022-11-25更新
|
416次组卷
|
5卷引用:云南省大理州民族中学、怒江州民族中学2024届高三上学期第一次联合考试数学试题
名校
4 . 如图,正方体
的棱长为
,
,
,
分别为
,
,
的中点,
点是正方形
内的动点.若
平面
,则
点的轨迹长度为________ .
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/2020/6/8/2480354550710272/2480444672139264/STEM/a9d015d0-8b4a-4937-8d99-0dc58d88046e.png)
您最近一年使用:0次
2020-06-08更新
|
976次组卷
|
3卷引用:江西省赣州市2020届高三适应性考试(二模)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: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
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
名校
解题方法
6 . 已知正方体
的棱长为
,
为棱
的中点,点
在正方形
内运动,且直线
平面
,则动点
的轨迹长度为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
7 . 如图,在长方体
中,底面是边长为
的正方形,侧棱长为
,
、
、
、
分别是棱
、
、
、
中点,
是底面
内一动点,若直线
与平面
不存在公共点,则三角形
面积的最小值为______ .
![](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/61128ab996360a038e6e64d82fcba004.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.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/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
![](https://img.xkw.com/dksih/QBM/2019/10/12/2310432546914304/2310578201026560/STEM/3b7972a2787d49e1bc19694ba8947254.png?resizew=143)
您最近一年使用:0次
2019-10-12更新
|
193次组卷
|
2卷引用:2019年9月湖北省黄冈市高三质量检测数学(理)试题
8 . 如图,在长方体
中,
,
是
(含端点)上一动点,则
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/25de2f01-5334-4a60-a374-fb371f278514.png?resizew=177)
①
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
②
与平面
所成角最小为45°
③三棱锥
体积为定值
④
与
所成的最大角为90°
上述命题中,正确的序号是______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf463f7f17333414ed8aeac269d508ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/25de2f01-5334-4a60-a374-fb371f278514.png?resizew=177)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8823177e737401071d6aedad22672405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7156eccdc0769adb348033afd2743e.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6545c18bf8a85c72ff361c88c7799d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
上述命题中,正确的序号是
您最近一年使用:0次
2011·北京东城·一模
解题方法
9 . 如图,在正方体
中,E,F,G,H,M分别是棱
,
,
的中点,点N在四边形EFGH的四边及其内部运动,则当N只需满足条件________ 时,就有
;当N只需满足条件________ 时,就有MN∥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9812da7973be4ef5b33326ebc87bceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f43488162b69d750f069b89a8b2d80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508dc6d9c91157836be679c0543cac.png)
![](https://img.xkw.com/dksih/QBM/2011/4/2/1570101236088832/1570101241184256/STEM/cee4b48e-9b86-488e-99a9-a0be7077aed7.png?resizew=191)
您最近一年使用:0次
解题方法
10 . 已知立方体
分别是棱
,
中点,从中任取两点确定的直线中,与平面
平行的有__________ 条.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca2df4004dd9c28db91e236eb401988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a92b81b5051305786ee367a83ffba06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b25f3ea33cc08b1e2a0d9c3a9dccaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8149669f297ecd19195e2dc357004af3.png)
![](https://img.xkw.com/dksih/QBM/2016/7/1/1572868616814592/1572868622540800/STEM/6c44762eaeee4fd3b887b16723068e77.png?resizew=160)
您最近一年使用:0次