1 . 如图,在四棱锥
中,底面ABCD为正方形,且侧棱PA⊥底面ABCD,PA=2AD.E,F,H分别是PA,PD,AB的中点,G为DF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/58d88241-48a0-47ae-832a-27407197fe0e.png?resizew=156)
(1)证明:
平面BEF;
(2)求PC与平面BEF所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/58d88241-48a0-47ae-832a-27407197fe0e.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b8c2721ada247b03f41f328539b301.png)
(2)求PC与平面BEF所成角的正弦值.
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2022-08-08更新
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2卷引用:第一章 空间向量与立体几何单元测试(巅峰版)
名校
2 . 如图,三棱柱ABC-A1B1C1中,侧棱AA1⊥平面ABC,△ABC为等腰直角三角形,∠BAC=90°,且AB=AA1=2,E,F分别为CC1,BC的中点.
![](https://img.xkw.com/dksih/QBM/2021/8/1/2777024024166400/2821869803700224/STEM/1605a151-da7e-4e64-b794-21a560e3bde1.png)
(1)若D是AA1的中点,求证:BD∥平面AEF;
(2)若M是线段AE上的任意一点,求直线B1M与平面AEF所成角的正弦的最大值.
![](https://img.xkw.com/dksih/QBM/2021/8/1/2777024024166400/2821869803700224/STEM/1605a151-da7e-4e64-b794-21a560e3bde1.png)
(1)若D是AA1的中点,求证:BD∥平面AEF;
(2)若M是线段AE上的任意一点,求直线B1M与平面AEF所成角的正弦的最大值.
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2021-10-04更新
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598次组卷
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4卷引用:人教A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 本章复习提升
人教A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 本章复习提升(已下线)第一章 空间向量与立体几何(本章复习提升)-2021-2022学年高二数学同步练习和分类专题教案(人教A版2019选择性必修第一册)安徽省亳州市第二中学2021-2022学年高二上学期第一次月考数学试题山东省济宁市2017-2018学年度高三上学期期末考试 数学(理)试题
解题方法
3 . 如图,在直三棱柱
中,
,
,点D,E,F分别为棱
,
,
的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/3f055186-6d32-4662-b08d-1c85d375a753.png?resizew=188)
(1)
平面DEF;
(2)平面
平面DEF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96a6b20a35af7755e5d90789ea862da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/3f055186-6d32-4662-b08d-1c85d375a753.png?resizew=188)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca714e3eade6d63792b729f4ff9f8316.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803fa75db3ac3a26a41e347dc4165026.png)
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解题方法
4 . 如图所示的平行六面体
中,已知
,
,
,
为
上一点,且
,点
棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2b5a914d-fbf1-499c-8feb-3424a4eec78f.png?resizew=215)
(1)用
,
,
表示
;
(2)若
,求
;
(3)若
,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1132330203ed3270a52e0fbd0f34e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13601fc499850fce16debbab6c627ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d76ebfa48fbd7a62488731294de8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28408efa93ec310ccdf156c02fc6c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14184f726fecb76ac6ab3f0b6dfd6f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2b5a914d-fbf1-499c-8feb-3424a4eec78f.png?resizew=215)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7559d65befe0b85c8929f57c9436cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4648d56ec5ba86c288bc22737250ba0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc14c781097654ee29b6b5435c31480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a114d968325e799e60de7ae82d1936.png)
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解题方法
5 . 如图,已知点P是平行四边形ABCD所在平面外一点,M、N分别是AB、PC的中点
平面PAD;
(2)在PB上确定一个点Q,使平面MNQ
平面PAD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)在PB上确定一个点Q,使平面MNQ
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
您最近一年使用:0次
2021-09-09更新
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1624次组卷
|
8卷引用:新疆哈密市第十五中学2021-2022学年高二上学期第一次月考数学试题
解题方法
6 . 如图,在棱长为a的正方体中,点M为A1B上任意一点,求证:DM∥平面CB1D1.
![](https://img.xkw.com/dksih/QBM/2020/10/10/2568104637374464/2569571144040448/STEM/c71c8b489c324a5687dbe4ee3b3213b7.png?resizew=183)
您最近一年使用:0次
2020-10-12更新
|
402次组卷
|
3卷引用:安徽省蚌埠市田家炳中学2020-2021学年高二上学期10月月考数学(文)试题
名校
解题方法
7 . 在等腰梯形
中,
,
,将它沿着两条高
,
折叠成如图所示的四棱锥
(
,
重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/93fe1829-bf0a-4bb4-9a6a-10d3176be62e.png?resizew=368)
(1)求证:
;
(2)设点
为线段
的中点,试在线段
上确定一点
,使得
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b06f824f3779f910448ae3a80f483d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3b9fe94b261d634f275a92d8b8cd2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/93fe1829-bf0a-4bb4-9a6a-10d3176be62e.png?resizew=368)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c182a9d9fd0a7023b710cd671d9468e7.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
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2020-11-26更新
|
2885次组卷
|
4卷引用:辽宁省盘锦市第二高级中学2020-2021学年高二第一学期第一次阶段性考试数学试题
辽宁省盘锦市第二高级中学2020-2021学年高二第一学期第一次阶段性考试数学试题江西省遂川中学2021-2022学年高二上学期第二次月考数学(理)试题(B卷)(已下线)第六章 立体几何初步(能力提升)-2020-2021学年高一数学单元测试定心卷(北师大2019版必修第二册)云南省北大附中云南实验学校2020-2021学年高一下学期期中考试数学试题
8 . 如图,正方体
,点
,
,
分别是棱
,
,
的中点,动点
在线段
上运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/88593270-17f9-4475-a131-3356f268fb5a.png?resizew=166)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/88593270-17f9-4475-a131-3356f268fb5a.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d45c10c00742e89d4123977720c0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
您最近一年使用:0次
2020-02-18更新
|
309次组卷
|
3卷引用:专练12 空间向量与立体几何综合检测卷(B卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)
(已下线)专练12 空间向量与立体几何综合检测卷(B卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)2023版 湘教版(2019) 选修第二册 过关斩将 第2章 本章复习提升2020届福建省龙岩市高三上学期期末教学质量检查数学(理)试题
名校
9 . 如图,已知在直三棱柱
中,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b0f37cd1-331e-4c2e-8237-dfefc4113f7d.png?resizew=155)
(1)在图中画出过
三点的截面,并说出截面图形的形状(不必说明画法与理由);
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48593b2bdb51550ec0a2b9d5893d36fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d508af23b2c772ab604c45b3eb081919.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b0f37cd1-331e-4c2e-8237-dfefc4113f7d.png?resizew=155)
(1)在图中画出过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5f302c1c2f7e1b46cad05594ed672e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9145a795e5f18846107a7355075bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcdb0295b373c6e306ca0dcf86f8b941.png)
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2019-10-29更新
|
621次组卷
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4卷引用:江西省南昌县莲塘第一中学2020-2021学年高二上学期期末数学(文)试题