名校
1 . 如图,在直四棱柱
中,四边形
是菱形,
,
,
,点E是棱
上的一点(与
,
不重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/22/0032f344-77a1-4315-9544-28e144f632db.png?resizew=137)
(1)求证:
;
(2)若二面角
的余弦值为
,求直线
与平面
所成角的正弦值.
![](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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/22/0032f344-77a1-4315-9544-28e144f632db.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd90dd9df8047d6093a7fb228245bec3.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b98d08cb05a894f940009f56c74d83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
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2023-01-19更新
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2卷引用:内蒙古阿拉善盟第一中学2022-2023学年高三上学期期末考试数学(理科)试题
名校
2 . 如图,已知三棱柱
中,平面
平面
,
,
,
,E,F分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/d9d3d69e-84c2-4178-b21f-75b0902eee96.png?resizew=189)
(1)证明:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4020513c097ba34df4b42e297f892cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e24261d71106c4a78fb187a1171bb6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204ffc27244d93a36696a938c1d85798.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/d9d3d69e-84c2-4178-b21f-75b0902eee96.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0538d15f20488fe686a92c79709c928.png)
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2023-01-19更新
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3卷引用:内蒙古赤峰二中2022-2023学年高二上学期期末考试数学(理)试题
名校
解题方法
3 . 如图所示,四棱锥
的底面
是矩形,
底面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/932dca6d-60d5-4a7f-95c2-6bb684b94f2e.png?resizew=160)
(1)证明:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa1c07becd03537beeb09a31745cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638d9cccb679214718224c3088ed4a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b279505327550bbb8077940fd44f01c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd358d23ced19c951ba670188ceaf15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/932dca6d-60d5-4a7f-95c2-6bb684b94f2e.png?resizew=160)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cfcf3b8cd4f355003350a9d45a1619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在直三棱柱
中,
,M、N分别是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/13134854-4f08-47a8-9c4e-28b84a07cd8f.png?resizew=142)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541db000edf20e5142fe6528b99bb5ba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/13134854-4f08-47a8-9c4e-28b84a07cd8f.png?resizew=142)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4c33d8708490972ffc11d8e9a6856.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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2023-01-03更新
|
511次组卷
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4卷引用:内蒙古自治区通辽市开鲁县第一中学2022-2023学年高二上学期期末数学试题
内蒙古自治区通辽市开鲁县第一中学2022-2023学年高二上学期期末数学试题北京市石景山区2022-2023学年高二上学期数学期末试题(已下线)模块四 专题6 暑期结束综合检测6(能力卷)(人教B)北京市昌平区首都师范大学附属中学昌平学校2023-2024学年高二上学期期中考试试数学试题
名校
5 . (理科)如图,四边形ABCD是边长为1的正方形,MD⊥平面ABCD,NB⊥平面ABCD,且
,E是MN的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/7b528c8f-8dfe-421f-970d-1a0d131d5191.png?resizew=186)
(1)求证:平面AEC⊥平面AMN;
(2)求二面角M-AC-N的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5254a8bb97154dc16c9435ef00ff5818.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/7b528c8f-8dfe-421f-970d-1a0d131d5191.png?resizew=186)
(1)求证:平面AEC⊥平面AMN;
(2)求二面角M-AC-N的余弦值.
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2023-01-03更新
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3卷引用:内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高一下学期期末考试数学试题
内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高一下学期期末考试数学试题甘肃省天水市第一中学2018届高三上学期第三阶段考试数学试题(已下线)江苏省七市2022届高三下学期第二次调研考试数学试题变式题17-22
10-11高三上·内蒙古·期末
名校
6 . 如下图,在三棱锥
中,
分别是
的中点,
,
.
(1)求证:
平面
;
(2)求异面直线
与
所成角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7f10e0c8af2d0d02a685f6f19e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5016f2cf1328d15d090597514b63045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/aedc281f-52e8-442c-9af4-20b48cea5b61.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2022-12-26更新
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25卷引用:2009—2010集宁一中学高三年级理科数学第一学期期末考试试题
(已下线)2009—2010集宁一中学高三年级理科数学第一学期期末考试试题(已下线)2010年郑州盛同学校高一下学期期末考试数学卷2014-2015学年广东省深圳市宝安区高一下学期期末考试数学试卷【市级联考】甘肃省兰州市2018-2019学年高一上学期第二片区丙组期末联考数学试题重庆市南岸区2019-2020学年高一上学期期末数学试题江苏省泰州市兴化中学2020-2021学年高二下学期期末模拟数学试题甘肃省定西市第一中学2022-2023学年高一上学期期末考试理科数学试题(已下线)2011-2012年湖南省衡阳市八中高二第三次月考考试理科数学(已下线)2012届广东省连州市连州中学高三12月月考理科数学试卷(已下线)2012-2013学年江西省白鹭洲中学高二第二次月考文科数学试卷(已下线)2012-2013学年江西省井冈山中学高二第四次月考文科数学试卷(已下线)2013届湖南省怀化市高三第二次模拟考试理科数学试卷新疆自治区北京大学附属中学新疆分校2018-2019学年高二10月月考数学试题【区级联考】天津市红桥区2019届高三一模数学(文)试题(已下线)专题02 各类角的证明与求解(第三篇)-备战2020年高考数学大题精做之解答题题型全覆盖山西省晋中市平遥县综合职业技术学校2018-2019学年高二(普通班)上学期期中数学试题2020届四川省成都市树德中学高三三诊模拟考试数学(文)试题广西北流市实验中学2020-2021学年高二上学期期中考试数学(理)试题天津市实验中学滨海学校2021-2022学年高二上学期10月月考数学试题天津市红桥区2019届高三下学期一模文科数学试题湖北省武汉市七校2022-2023学年高二上学期期中联考数学试题(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(1)-《考点·题型·技巧》江苏省南师大二附中、大桥中学2022-2023学年高二下学期5月联考数学试题(已下线)黄金卷01(已下线)第二章 立体几何中的计算 专题二 空间距离 微点2 点到平面距离【基础版】
7 . 如图,四棱锥
中,底面ABCD为菱形,PA⊥平面ABCD.
![](https://img.xkw.com/dksih/QBM/2022/11/8/3105210611130368/3106488183922688/STEM/2e00b963e98646f48f81963e4c34f8f7.png?resizew=243)
(1)求证:平面PAC⊥平面PBD;
(2)当PA=AB=2,∠ABC=
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2022/11/8/3105210611130368/3106488183922688/STEM/2e00b963e98646f48f81963e4c34f8f7.png?resizew=243)
(1)求证:平面PAC⊥平面PBD;
(2)当PA=AB=2,∠ABC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c16d2d9d22c4b34ddd965e26aa0d7.png)
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2022-11-10更新
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471次组卷
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4卷引用:内蒙古巴彦淖尔市衡越实验中学2022-2023学年高二上学期期末考试文科数学试题
8 . 如图,在四棱锥
中,底面为直角梯形,
,
底面
,且
分别为
的中点.
;
(2)求
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cf1949a53a014c451ee56801800f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5857b03445433bfe181ea446ecc4b51b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962515007ca98ad2d36557b60a42ad6f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a406f24b5131eb7da9127750319e52.png)
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5卷引用:内蒙古自治区赤峰市赤峰红旗中学2022-2023学年高一下学期期末数学试题
内蒙古自治区赤峰市赤峰红旗中学2022-2023学年高一下学期期末数学试题专题05 空间直线、平面的垂直-《期末真题分类汇编》(新高考专用)2006年普通高等学校招生考试数学(文)试题(浙江卷)(已下线)易错31题专练(沪教版2020必修三全部内容)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修三)黑龙江省大庆市东风中学2023-2024学年高二上学期开学考试数学试题
9 . 已知正四棱柱
,E为
中点,F为
中点.
为
与
的公垂线;
(2)求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35435fa442f3474e7d312c2360b28fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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2022-11-09更新
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928次组卷
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8卷引用:内蒙古包头市第四中学2022-2023学年高二上学期期末考试数学(理)试题
内蒙古包头市第四中学2022-2023学年高二上学期期末考试数学(理)试题2003 年普通高等学校招生考试数学试题(广东卷)2003 年普通高等学校招生考试数学(文)试题(全国卷)2003 年普通高等学校招生考试数学试题(辽宁卷)2003 年普通高等学校招生考试数学(文)试题(天津卷)(已下线)考点11 空间距离 2024届高考数学考点总动员 【讲】广东省汕头市潮阳黄图盛中学2023-2024学年高二上学期期中数学试题(已下线)第33题 空间距离解法笃定,向量方法建系第一(优质好题一题多解)
名校
解题方法
10 . 如图,已知梯形
,
//
,
,四边形
为正方形,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/9a030e54-21dc-4745-a474-a3da3d899530.png?resizew=177)
(1)求证:
平面
;
(2)点M在线段
上运动,求平面
与平面
夹角余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed645ab7488530b84db38031455c5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/9a030e54-21dc-4745-a474-a3da3d899530.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8acde6a4543f7c7dc745c542cda311b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
(2)点M在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-11-07更新
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530次组卷
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2卷引用:内蒙古通辽市重点校2022-2023学年高二上学期期末检测理科数学试题