名校
解题方法
1 . 已知,图中直棱柱
的底面是菱形,其中
.又点
分别在棱
上运动,且满足:
,
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
四点共面,并证明
∥平面
.
(2)是否存在点
使得二面角
的余弦值为
?如果存在,求出
的长;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa102f519d541f2e4d10a8975a41c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626db48efbecf4e318252ba13baff47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1357d24d53b523a55b3eea7b21fa16f1.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e807172fa9eca2416f92f341adc06165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
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2020-05-02更新
|
1264次组卷
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5卷引用:甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题
甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题2020届河南省高三第十次调研考试数学(理)试题江西省分宜中学、玉山一中等九校2019-2020学年高三联合考试数学理科试卷河北省衡水中学2019-2020学年高三下学期第十次调研数学(理)试题(已下线)1.4 空间向量的应用-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)
2 . 在四棱锥
中,平面
平面
,
为等边三角形,
,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/f1f9fdb1-7d4d-43a6-9769-373ae2e7ad05.png?resizew=226)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c313dff515240bc75d42f6687ac44cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/f1f9fdb1-7d4d-43a6-9769-373ae2e7ad05.png?resizew=226)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8d90d123fec1ae1b7b30dac9f88e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
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2020-02-09更新
|
867次组卷
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6卷引用:甘肃省天水市秦州区第一中学2019-2020学年高二上学期期末数学(理)试题
名校
3 . 1611年,约翰内斯·开普勒提出了“没有任何装球方式的密度比面心立方与六方最密堆积要高”的猜想.简单地说,开普勒猜想就是对空间中如何堆积最密圆球的解答.2017年,由匹兹堡大学数学系教授托马斯·黑尔斯(Thomas Hales)带领的团队发表了关于开普勒猜想证明的论文,给这个超过三百年的历史难题提交了一份正式的答案.现有大小形状都相同的若干排球,按照下面图片中的方式摆放(底层形状为等边三角形,每边4个球,共4层),这些排球共__________ 个,最上面球的球顶距离地面的高度约为__________
(排球的直径约为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2eb8ac733873fb3e728399ac856f16.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/8/0c87873d-c7f2-4a40-aad6-fc2f10261701.png?resizew=133)
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2020-04-24更新
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418次组卷
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2卷引用:2020届甘肃省第一次高考诊断考试理科数学试题
名校
4 . 如图,直三棱柱
中,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
平面
;
(2)已知
与平面
所成的角为30°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/04995d23-7b87-42b4-af22-6ed033682091.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319d234a0586478d4e73020d48b3a10.png)
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2020-05-13更新
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2756次组卷
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16卷引用:甘肃省永昌县第一中学2020-2021学年高三上学期第一次月考数学理试题
甘肃省永昌县第一中学2020-2021学年高三上学期第一次月考数学理试题【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)理科数学试题四川省广安市广安中学2019-2020学年高二9月月考(文)数学试题黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(理)试题江西省吉安市2019-2020学年高三上学期期中数学(理)试题江西省宜春市上高县第二中学2019-2020学年高三上学期11月月考数学(理)试题湖北省襄阳市2019-2020学年高二上学期期末数学试题2020届河北省衡水中学高三年级上学期五调考试数学(理科)试题2020届黑龙江省实验中学高三上学期期末考试数学(理)试题四川省棠湖中学2019-2020学年高三下学期第二次月考数学(理)试题(已下线)专题01 平行、垂直问题的证明(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东济南市历城第二中学2019-2020学年高一下学期开学考试数学试题江苏省无锡市江阴市高级中学2019-2020学年高二下学期期中数学试题2020届河北省衡水中学高三高考考前密卷(一)数学(理)试题湖北省宜昌市天问高中2019-2020学年高二(下)开学数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2.4 二面角
5 . 如图,底面
是等腰梯形,
,
,点
为
的中点,以
为边作正方形
,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/44fd4e14-d88a-497b-abc6-19a61028d1cb.png?resizew=155)
(1)证明:平面
平面
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e62ca104bd39a1646922b5836f1826b.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc7ee0ef8945ba1b90e59aed7cab889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bc259913bf02ed076530d2890c3620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/44fd4e14-d88a-497b-abc6-19a61028d1cb.png?resizew=155)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc7ee0ef8945ba1b90e59aed7cab889.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
2020-03-09更新
|
576次组卷
|
3卷引用:2020届甘肃省白银市靖远县高三第一次联考数学(文)试题
6 . 如图所示,在四棱锥P-ABCD中,PA⊥底面ABCD,AB⊥AD,AC⊥CD,∠ABC=60°,PA=AB=BC,E是PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/a50c5807-f76f-4264-a768-474742e199c2.png?resizew=164)
(1)求证:AE⊥平面PCD;
(2)求PB和平面PAD所成的角的大小;
(3)求二面角A-PD-C的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/a50c5807-f76f-4264-a768-474742e199c2.png?resizew=164)
(1)求证:AE⊥平面PCD;
(2)求PB和平面PAD所成的角的大小;
(3)求二面角A-PD-C的正弦值.
您最近一年使用:0次
2019-02-09更新
|
1323次组卷
|
9卷引用:2015-2016学年甘肃省兰州一中高一上学期期末数学试卷2
2015-2016学年甘肃省兰州一中高一上学期期末数学试卷2(已下线)2010年河南省卫辉市高级中学高一第三次月考数学试卷(已下线)2012届山东省莘县实验高中高三一轮复习质量检测理科数学(已下线)2012-2013学年广东省广州六中高一上学期期末考试数学试卷2015-2016学年河南省许昌市三校高一上学期第三次考试数学试卷2016-2017学年河北冀州市中学高二上开学测数学理试卷江西省玉山县第一中学2016-2017学年高二下学期第一次考试数学(理)试题(已下线)1.2.4 第2课时 两平面垂直的判定(课后作业)-2018-2019版数学创新设计课堂讲义同步系列(苏教版必修2)黑龙江省大庆实验中学2019-2020学年高二上学期开学考试数学(理)试题
7 . 如图,已知AA1⊥平面ABC,BB1∥AA1,AB=AC=3,BC=2
,AA1=
,BB1=2
,点E和F分别为BC和A1C的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/f43e5e90-fce3-4a30-8470-0af9db6c8394.png?resizew=115)
(1)求证:EF∥平面A1B1BA;
(2)求直线A1B1与平面BCB1所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/f43e5e90-fce3-4a30-8470-0af9db6c8394.png?resizew=115)
(1)求证:EF∥平面A1B1BA;
(2)求直线A1B1与平面BCB1所成角的大小.
您最近一年使用:0次
名校
8 . 在平面直角坐标系
中,已知圆
的方程为
,
点的坐标为
.
(1)求过点
且与圆
相切的直线方程;
(2)过点
任作一条直线
与圆
交于不同两点
,
,且圆
交
轴正半轴于点
,求证:直线
与
的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84269a13118a599708926a24c53d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1a4e2d41655ea7214d61bf6ed34e1b.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
您最近一年使用:0次
2019-02-06更新
|
2036次组卷
|
5卷引用:【市级联考】河南省驻马店市2018-2019学年高一上学期期末考试数学(理)试题
9 . 如图,在三棱柱
中,
,
,
为
的中点,点
在平面
内的射影在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/f0b7dd11-66d8-4bcf-969f-eee6f71f5e21.png?resizew=264)
(1)求证:
;
(2)若
是正三角形,求三棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f21c7c194c5bc2986a21fd441c81495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd57614136e2fc269f698a9c3904e31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/f0b7dd11-66d8-4bcf-969f-eee6f71f5e21.png?resizew=264)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eda94aeb495ebcb7380901d9ec2757.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88a11128d8f44ccc4f3d1cfdd7a9291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2019-01-30更新
|
1944次组卷
|
8卷引用:【校级联考】广东省华南师范大学附属中学、广东实验中学、广雅中学、深圳中学2019届高三上学期期末联考数学(文)试题
名校
解题方法
10 . 如图所示,在梯形
中,
∥
,
⊥
,
,
⊥平面
,
⊥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/c32e0b67-73e3-402a-83ba-a0731218d8c0.png?resizew=163)
(1)证明:
⊥平面
;
(2)若
,求点
到平面
的距离.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/c32e0b67-73e3-402a-83ba-a0731218d8c0.png?resizew=163)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2019-07-11更新
|
3909次组卷
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5卷引用:甘肃省天水市一中2020届高三一轮复习第一次模拟考试文科数学试题