1 . 如图,正方体
的棱长为1,线段
上有两个动点
,且
.’
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/5df5a10e-0952-4e1d-bab1-13557e786865.png?resizew=168)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)求三棱锥
的体积
(3)求异面直线
所成的角的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e438a162ed349f7f25333e8f6c044e6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/5df5a10e-0952-4e1d-bab1-13557e786865.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
(3)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268544817735d20ffbceef3b26db5dde.png)
您最近一年使用:0次
名校
2 . 如图,在三棱锥
中,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6aaf1f70-a95e-4a8a-970c-0fbf28e85ac1.png?resizew=188)
(1)证明:
平面ABC;
(2)若E是棱AC上的动点,当
的面积最小时,求SC与平面SDE所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145162491eef96e8ecdf1c0ea757cb87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214bfde0e33195dcea96e6aa22b271e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189c5df57466c011fe2d98f1540af294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f39bd910a7380c1f72e90537b875108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6aaf1f70-a95e-4a8a-970c-0fbf28e85ac1.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660f8143dbe1d2314469293efba6e98f.png)
(2)若E是棱AC上的动点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b09c565f36db58a4482b6d8621aaae5.png)
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2022-10-20更新
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4卷引用:黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题
黑龙江省哈尔滨市第九中学校2022-2023学年高二10月月考数学试题甘肃省武威第六中学2022-2023学年高三上学期第三次过关考试理科数学试题(已下线)陕西省宝鸡市金台区2022-2023学年高二上学期期末理科数学试题(已下线)8.6.2直线与平面垂直的性质定理(第2课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
名校
3 . 在多面体
中,平面
平面ABCD,EDCF是面积为
的矩形,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/8/26/3052759954268160/3053455803826176/STEM/4563ea97675a45c8bdfc6abaffa26254.png?resizew=203)
(1)证明:
.
(2)求平面EDCF与平面EAB夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fc1129846f37afdafd751627c450d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ea464a0929a33bedd2ee95cdb66ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a75b1354b8b783a65ee5e3bc596a976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/2022/8/26/3052759954268160/3053455803826176/STEM/4563ea97675a45c8bdfc6abaffa26254.png?resizew=203)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cade9d1bac990f2014ff8310613e2613.png)
(2)求平面EDCF与平面EAB夹角的余弦值.
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2022-08-27更新
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7卷引用:黑龙江省部分学校2022-2023学年高三上学期8月联考数学试题
2022高三·全国·专题练习
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4 . 在正方体
中,如图E、F分别是
,CD的中点,求证:
平面ADE;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36df8302f33f07a69cef14c3b822902.png)
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2022-08-20更新
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6卷引用:黑龙江省鸡西市第四中学2022-2023学年高二上学期第一次月考数学试题
黑龙江省鸡西市第四中学2022-2023学年高二上学期第一次月考数学试题(已下线)专题32 空间向量及其应用-3(已下线)第05讲 空间向量及其应用 (高频考点—精讲)-2(已下线)专题10 空间向量与垂直关系(重点突围)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)苏教版(2019)选择性必修第二册课本例题6.3 空间向量的应用广东省东莞市弘林高级中学2023-2024学年高二上学期9月月考数学试题(A)
名校
解题方法
5 . 在直三棱柱
中,AB=AC,D为BC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/1cb3d81c-a5ce-48ce-abd7-39d9f4ce85a9.png?resizew=144)
(1)求证:AD⊥平面
;
(2)若
,BC=2,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/1cb3d81c-a5ce-48ce-abd7-39d9f4ce85a9.png?resizew=144)
(1)求证:AD⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ae8a050d7159d4296c2409e5bc0bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44dc7e4469c1fc443464c105b20f1224.png)
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2022-07-23更新
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2卷引用:黑龙江省哈尔滨市第九中学校2021-2022学年高一下学期期末数学试题
名校
6 . 如图,在四棱锥
中,底面
是边长为2的菱形,
,
是正三角形,
为线段
的中点,点
为棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5694b0d5-c7e0-4245-9102-23089157ed41.png?resizew=183)
(1)求证:平面
平面
;
(2)若平面
平面
.
①当点
恰为
中点时,求异面直线
与
所成角的余弦值;
②在平面
内确定一点
,使
的值最小,并求此时
的值.
![](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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5694b0d5-c7e0-4245-9102-23089157ed41.png?resizew=183)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
②在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb64f6a63cc7cf145b0e8de061491117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212fafcdb754da6728a8b06fded23955.png)
您最近一年使用:0次
2022-07-16更新
|
1158次组卷
|
4卷引用:黑龙江省齐齐哈尔市2021-2022学年高一下学期期末数学试题
名校
解题方法
7 . 在如图所示的几何体中,四边形ABCD是正方形,平面ABCD⊥平面PAB,E,F分别是线段AD,PB的中点,
.证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ceee8839-7f73-4488-9191-c59704a48bfc.png?resizew=158)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面PDC;
(2)PB⊥平面DEF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ceee8839-7f73-4488-9191-c59704a48bfc.png?resizew=158)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
(2)PB⊥平面DEF.
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2022-07-08更新
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5卷引用:黑龙江省绥化市望奎县第一中学2021-2022学年高一下学期期末数学试题
黑龙江省绥化市望奎县第一中学2021-2022学年高一下学期期末数学试题湖北省鄂州市2021-2022学年高一下学期期末数学试题河南省名校联盟2022-2023学年高二上学期开学考试数学试题(已下线)7.2 空间几何中的垂直(精练)(已下线)7.1 空间几何中的平行与垂直(精讲)
名校
8 . 在三棱台
中,
,
, 侧面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c93878e0291b61da2f432feadb70b1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/98cf9ec8-5dad-41b5-b63d-78d595ec1fcf.png?resizew=162)
(1)求证:
平面
;
(2)求证:
是直角三角形;
(3)求直线
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/0d0543f5a584b4b6e4714a467a104c96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/973bc82f603ff7b3ab28bd238fbe8c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c93878e0291b61da2f432feadb70b1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/98cf9ec8-5dad-41b5-b63d-78d595ec1fcf.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5f9ef971747d2d5bbc5823797a7a65.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2022-06-27更新
|
1446次组卷
|
4卷引用:黑龙江省大庆市大庆铁人中学2021-2022学年高一下学期期末数学试题
黑龙江省大庆市大庆铁人中学2021-2022学年高一下学期期末数学试题浙江省温州市2021-2022学年高一下学期期末数学试题(A卷)(已下线)微专题15 轻松搞定线面角问题(已下线)期末专题05 立体几何大题综合-【备战期末必刷真题】
名校
解题方法
9 . 如图,在三棱柱
中,
平面ABC,
,
,
,点D,E分别在棱
和棱
上,且
,
,M为棱
的中点.
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0268d04b9dea7629af27af9a0285a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8973bcb7d87303a0b5fba04a801019b9.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537b25d7d8d13a6ef990c7c370def871.png)
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2022-06-10更新
|
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|
8卷引用:黑龙江省哈尔滨市第九中学校2022届高三第三次模拟考试数学(文科)试题
黑龙江省哈尔滨市第九中学校2022届高三第三次模拟考试数学(文科)试题内蒙古赤峰市2021-2022学年高一下学期期末考试数学(文)试题(已下线)专题31 直线、平面垂直的判定与性质-1广西2023届高三上学期开学摸底考试数学(文)试题广西柳州市鹿寨县鹿寨中学2023届高三上学期开学摸底考试数学(文)试题(已下线)8.6.2 直线与平面垂直(1) -2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)第06讲 空间直线﹑平面的垂直(一)-《知识解读·题型专练》(已下线)第十一章:立体几何初步章末重点题型复习(2)-同步精品课堂(人教B版2019必修第四册)
名校
10 . 已知四棱锥
满足:四边形ABCD为正方形,△PAD为等边三角形,且平面PAD⊥平面ABCD,
,E为PA的中点.
平面BDE;
(2)求直线PC和平面ABCD所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
(2)求直线PC和平面ABCD所成角的正切值.
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2022-05-24更新
|
2090次组卷
|
5卷引用:黑龙江省哈尔滨师范大学青冈实验中学校2021-2022学年高一下学期期末考试数学试题