解题方法
1 . 已知正方体
的棱长为
是空间中的一动点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0342946a0f827001a879cad686d1cf68.png)
A.若点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
B.平面![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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名校
解题方法
2 . 正四棱锥
中,各棱长均为1,
过点M,N,Q的平面交PD于点S,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63599dde9c916906138294b26e39c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4648a19cafbfff36232bdbc870c7961f.png)
A.![]() |
B.点S到平面PMQ的距离为![]() |
C.平面MNQ与平面ABCD夹角的余弦值为![]() |
D.两个四棱锥![]() ![]() ![]() |
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3 . 如图,四棱锥
中,二面角
的大小为
,
,
,
是
的中点.
平面
;
(2)若直线
与底面
所成的角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6380f35cdd3050759a4a91b8637adc1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a963651010d49547f357eb102571808b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b94b15559e9532322cf43ef02109f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54cf75bbfc9db93d27937c8b8e977b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d387d228f512ada68fc79c9d5775b077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbbccfcae3f2523849577320fe331dc.png)
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2024-04-18更新
|
1689次组卷
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4卷引用:山西省天一名校2023-2024学年高三下学期联考仿真模拟(二模)数学试题
山西省天一名校2023-2024学年高三下学期联考仿真模拟(二模)数学试题海南省海南中学2024届高三下学期第九次半月考数学试题(已下线)压轴题04立体几何压轴题10题型汇总-1(已下线)大招2 空间几何体中空间角的速破策略
解题方法
4 . 已知正方体
的棱长为1,点
满足
,
(
与
三点不重合),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ae7072624587654d162548a80d7a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6da55fea580ca1efa66cb4de0d24a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ccc6b9e27a149ffb7b2196eda25bb0.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
5 . 如图,棱长为2的正方体
中,E,F分别为棱
的中点,G为线段
上的动点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/40506d94-4f2f-4dcc-8667-55f3b3ef4910.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afaa4776f2c9598c44f4b6b874afe1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/40506d94-4f2f-4dcc-8667-55f3b3ef4910.png?resizew=166)
A.三棱锥![]() |
B.存在点G,使得![]() |
C.G为![]() ![]() |
D.点F到直线EG距离的最小值为![]() |
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6 . 在棱长为
的正方体
中,
是棱
的中点,点
在棱
上运动(不与端点重合),则下列结论正确的是( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
A.三棱锥![]() ![]() |
B.直线![]() ![]() ![]() |
C.三棱锥![]() ![]() |
D.平面![]() ![]() ![]() |
您最近一年使用:0次
解题方法
7 . 如图,在斜三棱柱
中,
是边长为2的正三角形,且四棱锥
的体积为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a38bea62-ec09-4a80-b5ee-88e774fe334f.png?resizew=146)
(1)求三棱柱
的高;
(2)若
,平面
平面
为锐角,求平面
与平面
的夹角的余弦值.
![](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/f2d0727de4c16b53b4bb6ab370afde6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/a38bea62-ec09-4a80-b5ee-88e774fe334f.png?resizew=146)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c68bfddc0f0df9ddd0aae3cad6fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
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2023-11-21更新
|
1663次组卷
|
3卷引用:山西省2023-2024学年高三11月联合考试模拟预测数学试题
名校
解题方法
8 . 已知正方体
的棱长为2,P是空间中的一动点,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-10-16更新
|
426次组卷
|
7卷引用:山西省部分名校2023-2024学年高二上学期10月联考数学试题
山西省部分名校2023-2024学年高二上学期10月联考数学试题辽宁省部分高中2023-2024学年高二上学期10月月考数学试题云南省部分名校2024届高三上学期10月联考数学试题江西省萍乡中学、新余市第一中学2023-2024学年高二上学期创新班联考数学试题新疆兵团地州学校2023-2024学年高二上学期期中联考数学试题(已下线)考点16 立体几何中的最值问题 2024届高考数学考点总动员【练】(已下线)第二章 立体几何中的计算 专题三 空间面积的计算 微点2 空间面积的计算综合训练【基础版】
名校
9 . 如图,在四棱柱
中,四边形
是平行四边形,
,
,
,
,
为
的中点,且
.
(1)求证:
平面
;
(2)若平面
与平面
的夹角的余弦值为
,求三棱锥
的体积.
![](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/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c078a10649b3a953631690021aa59879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fc4baf66de980a95f267051e6b190d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/f1a7d905-8650-42ac-910a-75b64a3ee109.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6ab0386dde0643de8caf33f946072f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924d32b574fe69e43724304cf39513e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35ac94f0ea5d79ae4530f5a3116f670.png)
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2023-10-13更新
|
897次组卷
|
3卷引用:山西省孝义市2023-2024学年高二上学期10月月考数学试题
名校
解题方法
10 . 如图所示,在四棱锥
中,底面
为直角梯形,
∥
、
、
、
,
、
分别为
、
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/8372c1fd-7a2e-46d0-82d4-828a5e99b5da.png?resizew=184)
(1)证明:平面
平面
;
(2)若
与
所成角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639bec6242a4b3f7bfb4b7033a67328c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829fc6685b59fdc609f32f30ebd9e6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/8372c1fd-7a2e-46d0-82d4-828a5e99b5da.png?resizew=184)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a590bdfe296689fc138d8995deae2026.png)
您最近一年使用:0次
2023-11-05更新
|
2818次组卷
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13卷引用:山西省运城市稷山县稷山中学2023-2024学年高二上学期11月月考数学试题
山西省运城市稷山县稷山中学2023-2024学年高二上学期11月月考数学试题新疆克拉玛依市2022届高三下学期第三次模拟检测数学(理)试题广东省广州市奥林匹克中学2021-2022学年高二下学期6月月考数学试题辽宁省铁岭市昌图县第一高级中学2021-2022学年高一下学期期末数学试题(已下线)1.2.4 二面角(已下线)第4讲 空间向量的应用 (3)(已下线)第07讲 空间向量的应用 (2)重庆市北碚区缙云教育联盟2024届高考零诊数学试题(已下线)四川省成都市第七中学2023-2024学年高二上学期12月月考数学试题北京市丰台区2023-2024学年高二上学期期末模拟数学试题江西省上饶市广丰区南山中学2023-2024学年高二上学期期末模拟数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(三)新疆维吾尔自治区阿克苏地库车市第二中学2023-2024学年高二上学期第二次月考(12月)数学