名校
解题方法
1 . 如图,在正方体
中,M、N、P分别是
、
和AB的中点,则下列关系:
①BM⊥AB;
②BM∥平面
;
③
;
④
⊥平面
,
正确的编号为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
①BM⊥AB;
②BM∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274b5872d5b9cff3b4be8fe43e74d216.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649655c62a1aa10ea1d6509db9c1cab1.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd94d3c3765c52e2d6375f1959686430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274b5872d5b9cff3b4be8fe43e74d216.png)
正确的编号为
您最近一年使用:0次
2022-11-16更新
|
574次组卷
|
13卷引用:上海市晋元高级中学2023-2024学年高二上学期10月月考数学试题
上海市晋元高级中学2023-2024学年高二上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2020-2021学年高二下学期开学考试数学试题上海市市西中学2022-2023学年高二上学期开学考数学试题(已下线)专题02简单几何体(7个考点)【知识梳理+解题方法+专题过关】-2022-2023学年高二数学上学期期中期末考点大串讲(沪教版2020必修第三册+选修一)(已下线)第05讲线线、线面、面面垂直的判定与性质(核心考点讲与练)(1)第10章 空间直线与平面 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)10.3 直线与平面间的位置关系(第2课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)上海市朱家角中学2023-2024学年高二上学期期中数学试题上海市市北中学2023-2024学年高二上学期期中考试数学试题天津市南开中学2017-2018学年度高二第一学期期中考试数学(理)试题(已下线)专题8.12 空间直线、平面的垂直(一)(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)8.6.3平面与平面垂直——课后作业(巩固版)(已下线)8.6.1直线与直线垂直+8.6.2直线与平面垂直——课后作业(巩固版)
名校
2 . 如图,三棱柱
中,
,
,
,点M,F分别为BC,
的中点,点E为AM的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/ecc898ed-c182-4773-a131-9f844eda35bd.png?resizew=252)
(1)证明:
;
(2)证明:
平面
;
(3)求直线EF与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10d461a7c0b86a2f09c2ea17f38260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9de9676ad1d41bd828a8fcbd100d940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/ecc898ed-c182-4773-a131-9f844eda35bd.png?resizew=252)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0a886f1192d450ced9fd875e78425e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(3)求直线EF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2022-11-13更新
|
496次组卷
|
3卷引用:上海市曹杨第二中学2023-2024学年高二上学期10月月考数学试题
解题方法
3 . 在正方体ABCD﹣A1B1C1D1中,E是BC1的中点,求证:DE∥平面AB1D1.
您最近一年使用:0次
名校
4 . 如图,已知四边形ABCD为矩形,PD
底面ABCD,PD=DC=2AD=2,E是PC的中点,过E点作EF
PB交PB于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/927faa7f-16f1-4abb-a183-668422b3d1c5.png?resizew=162)
(1)求证:PA
平面EDB;
(2)求证:PB
ED;
(3)求BD与平面EFD所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/927faa7f-16f1-4abb-a183-668422b3d1c5.png?resizew=162)
(1)求证:PA
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)求证:PB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(3)求BD与平面EFD所成角.
您最近一年使用:0次
名校
5 . 在梯形
中,
,
,
,P为AB的中点,线段AC与DP交于O点(如图1).将
沿AC折起到
位置,使得平面
平面
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7f4fd035-e109-4774-8bba-06663dbfbeae.png?resizew=495)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
平面
;
(2)求二面角
的大小;
(3)线段
上是否存在点Q,使得CQ与平面
所成角的正弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89ee6576c35c682bcb0eff43bd958d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6829c6214e60edbfbf1e31601c6bcb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3c5eea67eecdd13a2e6cd60d1d67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7f4fd035-e109-4774-8bba-06663dbfbeae.png?resizew=495)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde275553b4e49f5adffe606875c6ec3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845b65a3d273b6792d63f3d925cd4bc0.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be451ce5fad246389ccf4864929d81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e95fa1c3bcd3d0464fcadf248e90ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80dbac2006d30c49943f0241fd976eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b188172a322d69106c638e1603ac13f.png)
您最近一年使用:0次
2022-11-08更新
|
558次组卷
|
6卷引用:上海市青浦高级中学2022-2023学年高二上学期12月质量检测数学试题
上海市青浦高级中学2022-2023学年高二上学期12月质量检测数学试题北京市第五十七中学2021-2022学年高二上学期期末数学试题(已下线)第03讲 空间向量的应用-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题广东省广州市第十六中学2022-2023学年高二上学期期中数学试题广东省广州市第五中学2023-2024学年高二上学期期中数学试题
解题方法
6 . 如图,在四棱锥
,底面
是正方形,侧面
底面
,且
,若
、
分别为
、
的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/facb2261-cd7d-4e3d-aac2-ddce94e97cdb.png?resizew=219)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18037eb1473bf29cbeadabf51fca022f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/facb2261-cd7d-4e3d-aac2-ddce94e97cdb.png?resizew=219)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92dc7c262bba52d1b97c17c6d07e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
名校
7 . 如图,在直三棱柱
中,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/7a096403-e09e-4693-be92-aecc0f275368.png?resizew=222)
(1)求证:
平面
;
(2)若
,求异面直线
与
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdaa2495981cf1f87339efd7911f56f.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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/7a096403-e09e-4693-be92-aecc0f275368.png?resizew=222)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1be642ddd61c3ad26bcbe2dc42e3512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次
2022-10-14更新
|
343次组卷
|
2卷引用:上海市华东师范大学第一附属中学2023届高三上学期10月月考数学试题
名校
解题方法
8 . 在正方体
中,M,N,P分别为
,AD,
的中点,棱长为1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/e146b5d5-617e-49a1-9ba0-cc78811c0c1c.png?resizew=176)
(1)求证:
平面
;
(2)过M,N,P三点作正方体的截面,画出截面(保留作图痕迹),并计算截面的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adfcfa3dbc655af0f42d8773eb7710f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/e146b5d5-617e-49a1-9ba0-cc78811c0c1c.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d80ed37728f5933020ccb894541e857.png)
(2)过M,N,P三点作正方体的截面,画出截面(保留作图痕迹),并计算截面的周长.
您最近一年使用:0次
2022-10-11更新
|
552次组卷
|
3卷引用:上海市洋泾中学2022-2023学年高二上学期10月质量检测数学试题
名校
解题方法
9 . 如图,在四棱锥
中,底面ABCD是边长为1的菱形,
,
底面ABCD,
,M为OA的中点,N为BC的中点.
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074962496315392/3077487675555840/STEM/89ab3db848a149f798a7b2df16dded4a.png?resizew=180)
(1)证明:直线
面OCD;
(2)求点B到平面OCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d01872723102269f05c9d1b77c6e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074962496315392/3077487675555840/STEM/89ab3db848a149f798a7b2df16dded4a.png?resizew=180)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
(2)求点B到平面OCD的距离.
您最近一年使用:0次
2022-09-30更新
|
699次组卷
|
2卷引用:上海市松江二中2023届高三上学期9月月考数学试题
名校
10 . 在2021年6月17日,神舟十二号载人飞船顺利升空并于6.5小时后与天和核心舱成功对接.如图,是神舟十二号飞船推进舱及其推进器的简化示意图,半径相等的圆
,
,
,
,与圆柱
底面相切于A,
,
,
四点,且圆
与
,
与
,
与
,
与
分别外切,线段
为圆柱
的母线.点
线段
中点,点
在线段
上,且
.已知圆柱
,底面半径为2,
.
![](https://img.xkw.com/dksih/QBM/2022/9/24/3073394627772416/3077134407106560/STEM/1a9d11fdcd454718bc26122f5c85a8d9.png?resizew=249)
![](https://img.xkw.com/dksih/QBM/2022/9/24/3073394627772416/3077134407106560/STEM/616638412e2e4043a9271d45e1fa5d2e.png?resizew=304)
(1)求证:
平面
;
(2)线段
上是否存在一点
,使得
平面
?若存在,请求出
的长,若不存在,请说明理由;
(3)如图,是飞船推进舱与即将对接的天和核心舱的相对位置的简化示意图.天和核心舱为底面半径为2的圆柱
,它与飞船推进舱共轴,即
,
,
,
共线.核心舱体两侧伸展出太阳翼,其中三角形
为以
为斜边的等腰直角三角形,四边形
为矩形.已知推进舱与核心舱的距离为4,即
,且
,
.在对接过程中,核心舱相对于推进舱可能会相对作出逆时针旋转的运动,请你求出在舱体相对距持不变的情况下,在舱体相对旋转过程中,直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f904e5f274c559bdba741df035ed3461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5991360cbe7b47dc6b44ae4c323bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1ac49b4139636fb1809fe970b23a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1a0fd1ad044a9ecfcba672779bd678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f904e5f274c559bdba741df035ed3461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f904e5f274c559bdba741df035ed3461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5991360cbe7b47dc6b44ae4c323bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5991360cbe7b47dc6b44ae4c323bb.png)
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![](https://img.xkw.com/dksih/QBM/2022/9/24/3073394627772416/3077134407106560/STEM/1a9d11fdcd454718bc26122f5c85a8d9.png?resizew=249)
![](https://img.xkw.com/dksih/QBM/2022/9/24/3073394627772416/3077134407106560/STEM/616638412e2e4043a9271d45e1fa5d2e.png?resizew=304)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)如图,是飞船推进舱与即将对接的天和核心舱的相对位置的简化示意图.天和核心舱为底面半径为2的圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3711953485a76de370a04756009a644a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e046095eefc95b26511f64d1cb3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cce6cac0fdd4b1a434af8bcaec8fef.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
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2022-09-29更新
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7卷引用:上海市五校2022-2023学年高二下学期3月联考数学试题
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