名校
解题方法
1 . 在棱长为2的正方体
中,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/555c771c-8b93-4469-a840-0d43cd9d9ac4.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68345111b4081c514cc15ee82167898f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02b7a2a4601a4a52dc2638845eae3b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/24/555c771c-8b93-4469-a840-0d43cd9d9ac4.png?resizew=152)
A.![]() |
B.三棱锥![]() |
C.若![]() ![]() ![]() |
D.三棱锥![]() ![]() |
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名校
2 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618f2f945043c0fc4b2bb492206d4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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解题方法
3 . 如图,P为圆锥的顶点,O是圆锥底面的圆心,为底面直径,
为底面圆O的内接正三角形,点E在母线
上,且
,
.
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)若点M为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
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2023-11-26更新
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1529次组卷
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5卷引用:河北省石家庄市第二中学2023-2024学年高二上学期期末第一次模拟考数学试题
河北省石家庄市第二中学2023-2024学年高二上学期期末第一次模拟考数学试题江苏省靖江高级中学2023-2024学年高二下学期3月月考数学试题山东省日照市2024届高三上学期期中校际联合考试数学试卷广东省珠海市第一中学2024届高三上学期期末模拟数学试题(已下线)专题15 立体几何解答题全归类(9大核心考点)(讲义)-2
名校
解题方法
4 . 在棱长为2的正方体
中,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.若![]() ![]() ![]() |
B.点![]() ![]() ![]() ![]() ![]() |
C.点![]() ![]() ![]() ![]() ![]() ![]() |
D.已知过点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2023-11-29更新
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294次组卷
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2卷引用:河北省保定市定州市2023-2024学年高二上学期期中数学试题
5 . 已知正方体
的棱长为1,H为棱
(包含端点)上的动点,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
A.二面角![]() ![]() |
B.![]() |
C.若O在正方形![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2023-11-06更新
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3卷引用:河北省邯郸市鸡泽县第一中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
6 . 如图,在三棱柱
中,底面
是边长为8的等边三角形,
,
,
,
在棱
上且满足
.
(1)求证:平面
平面
;
(2)若平面
与平面
夹角的余弦值为
,求三棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a02316ea0fa85a18ac5c3fb4a9a14d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02864602e30b261c2de2fffb52193a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064a04589ae680482d23c3b08f820917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffc2a946e72f26a8af584d8ead3a396.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/0773613d-9932-44bd-b7ba-84e6c90d3060.png?resizew=192)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecfe1bf6f7bfe17f9bd28e97b0147f6.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd4e447289888d9af05eb91a8af9581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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名校
解题方法
7 . 如图所示的八面体的表面是由2个全等的等边三角形和6个全等的等腰梯形组成,设
,
,有以下四个结论:其中正确的结论是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1bdb08d371f24f7b4aeae53f292050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/1d83d4bb-5aa1-4196-8d0e-2b9bfa30361c.png?resizew=153)
A.![]() ![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2023-10-13更新
|
177次组卷
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2卷引用:河北省衡水市武邑中学2023-2024学年高二上学期第一次月考数学试题
名校
解题方法
8 . 图,在三棱台
中,
是等边三角形,
,侧棱
平面
,点D是棱
的中点,点E是棱
上的动点(不含端点B).
(1)证明:平面
平面
;
(2)求平面
与平面
的夹角的余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee6b48346072cb2dd3df26cf733f010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/7f30a3f1-1a52-454c-8e3a-52b0bbc4bbfc.png?resizew=160)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce04b35c265cc9c48b60204bd2f718ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0ca7c25eceffc1c3515446f59396e1.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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2023-10-10更新
|
429次组卷
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7卷引用:河北省石家庄第十五中学2023-2024学年高二上学期期中数学试题
名校
解题方法
9 . 如图,在四棱锥
中,平面
平面
,底面
是矩形,
,
,
,点
是
的中点,则线段
上的动点
到直线
的距离的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e004715ae5b4f4a4272ed210ae460f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2686149cd09003b9dcccb51d81fe51ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
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2023-10-10更新
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8卷引用:河北省2023-2024学年高二上学期10月月考数学试题
河北省2023-2024学年高二上学期10月月考数学试题河南省洛阳市强基联盟2023-2024学年高二上学期10月联考数学试题(已下线)1.4.2 用空间向量研究距离、夹角问题【第二练】山东省菏泽市鄄城县第一中学2023-2024学年高二上学期12月月考数学试题湖南省常德市临澧县第一中学2023-2024学年高二下学期入学考试数学试题江苏省泰州中学2023-2024学年高二下学期期中考试数学试题江苏省扬州市第一中学2023-2024学年高二下学期5月教学质量调研评估数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点3 平面法向量求法及其应用综合训练【培优版】
名校
解题方法
10 . 如图,
为圆柱底面圆周上三个不同的点,
分别为半圆柱的三条母线,且
是
的中点,
分别为
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
平面
.
(2)若
是
上的动点(含弧的端点),求
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1921b3559a5f73426f0d78e401ecc75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7f10e0c8af2d0d02a685f6f19e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a773f779cd892616a4ff68d3715f173.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/9dcbcca4-2b51-4993-aa32-884b622028af.png?resizew=90)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d9a7eb9395b5c7e9668be90d4d1dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a3d5d669ac76a2ffb07da81d949adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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2023-10-05更新
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4卷引用:河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题
河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题河北省邢台市河北南宫中学2023-2024学年高二上学期第一次月考数学试题广东省深圳市名校2023-2024学年高二上学期期中联考数学试题(已下线)难关必刷01 空间向量的综合应用-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)