名校
1 . 在正四棱柱
中,
,
是棱
上的中点.
(1)求证:
;
(2)异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b66218bbfb24acee762d795831e42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/56f1fa7d-2b62-4c27-ab33-8062918930d5.png?resizew=130)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ab924e3692515bd8be4c36472a959a.png)
(2)异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2023-10-20更新
|
2739次组卷
|
16卷引用:北京市丰台区2022-2023学年高二上学期数学期末练习数学试题
北京市丰台区2022-2023学年高二上学期数学期末练习数学试题四川省雅安市雅安中学2022-2023学年高二下学期期中数学(理)试题第一章 空间向量与立体几何 (单元测)福建省仙游县枫亭中学2022-2023学年高二下学期期中考试数学试题河南省郑州市基石中学2022-2023学年高二下学期期中数学试题江苏省南通市如皋中学2024届高三创新实验班夏令营数学试题(已下线)第三章 空间向量与立体几何(基础巩固检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)北京市朝阳区东北师范大学附属中学朝阳学校2023-2024学年高二上学期第一次学习质量监测与反馈数学试题湖南省长沙市德成学校2023-2024学年高二上学期10月月考数学试题海南省川绵中学2023-2024学年高二上学期10月第一次月考数学试题山西省运城市景胜中学2023-2024学年高二上学期10月月考数学试题(A卷)广东省佛山市顺德德胜学校2023-2024学年高二上学期期中数学试题广西壮族自治区桂林市灵川县广西师大附中2023-2024学年高二上学期段考(期中)数学试题河南省三门峡市渑池县第二高级中学2023-2024学年高二上学期第二次月考(11月)数学试题湖南省张家界市民族中学2023-2024学年高二上学期第二次月考数学试题(已下线)考点12 空间角 2024届高考数学考点总动员 【讲】
名校
解题方法
2 . 如图,四棱锥
中,
底面
,底面
是边长为2的菱形,
,F为CD的中点,
,以B为坐标原点,
的方向为x轴的正方向,建立如图所示的空间直角坐标系.
(1)写出B,D,P,F四点的坐标;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083a20abb668d4c26fe5039bd108b40a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/4d1f2edb-dabe-4809-986b-eb15bec12663.png?resizew=170)
(1)写出B,D,P,F四点的坐标;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ca335ca0d8c25656d8d711b9429968.png)
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2023-10-14更新
|
783次组卷
|
2卷引用:安徽省高二名校阶段检测联考2023-2024学年高二上学期10月月考数学试题
名校
3 . 如图,三棱锥
中的三条棱
两两互相垂直,
,点
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/7ab9e002-ef32-4e3e-b432-a420b0aaa507.png?resizew=158)
(1)证明:
平面
.
(2)若
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1361092e790e4154a14aea9d0db65a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea6ce40f9bd9083dd8e40822f21ebb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe9b0c00cab139524b79ab2847e462e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/7ab9e002-ef32-4e3e-b432-a420b0aaa507.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42de572d68ded125eccccc512c4fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-10-10更新
|
1654次组卷
|
3卷引用:河南省周口市项城市第三高级中学2023-2024学年高二上学期第一次月考数学试题
解题方法
4 . 如图,在空间直角坐标系
中,四棱柱
为长方体,
,点
,
分别为
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd407cdb6c758cdbe7e7216544f85b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce34c05c1445e027e9fc009907046e7e.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/c81e73dcdb8d3c374100ec83bf6983f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c8b9d5680c06f9e28c311d67cfadd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/10/c518b1ae-4ba9-4eee-960b-107167e5e2c1.png?resizew=181)
您最近一年使用:0次
2023-08-10更新
|
1414次组卷
|
3卷引用:江苏省徐州市铜山区铜北中学2022-2023学年高一下学期3月学情调查数学试题
2023高三·全国·专题练习
解题方法
5 . 两平面的法向量为
,
,求两平面所成锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376d976069aad337f6ef96dc93f29131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9527044b6948bf34d88d2fec3fd249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
6 . 如图,已知多面体
中,
均垂直于平面
,
,
,
.请用空间向量的方法解答下列问题:求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192d435f8d96adc954c50c7e4baf784b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aedf65d7d930fdb972d4802c0dea8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fbc0abdc242efef1ddb98cc4005550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/5394ea48-bf01-4c70-9fd6-f82bc35d66fb.png?resizew=147)
您最近一年使用:0次
名校
7 . 如图所示,在多面体
中,四边形
均是边长为1的正方形,E为
的中点,过
,D,E的平面交
于F.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/88787091-cfb2-49f8-aec6-c0c6f254edf3.png?resizew=196)
(1)求二面角
的余弦值;
(2)试确定点F的位置,并求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041e627e7cf1e55c5b3620444d2e9430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cae66ca62dadce55327a85f486433b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/88787091-cfb2-49f8-aec6-c0c6f254edf3.png?resizew=196)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165d8a626561c01210793e42859f7ed0.png)
(2)试确定点F的位置,并求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
8 . 如图,圆柱上,下底面圆的圆心分别为
,
,该圆柱的轴截面为正方形,三棱柱
的三条侧棱均为圆柱的母线,且
,点
在轴
上运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/16320c31-ce99-46e9-9397-f9a2951ace6b.png?resizew=131)
(1)证明:不论
在何处,总有
;
(2)当
为
的中点时,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f67c897b31dc0889695594e59d88038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/16320c31-ce99-46e9-9397-f9a2951ace6b.png?resizew=131)
(1)证明:不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7ef46a372d4c6481a7bc245c5d0aa2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a571745474520e3db9cb68c76585f63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fbde8c306b6cfcb7c68ccf01e00b49.png)
您最近一年使用:0次
2022-12-08更新
|
890次组卷
|
4卷引用:山东省泰安市2022-2023学年高二上学期期中考试数学试题
山东省泰安市2022-2023学年高二上学期期中考试数学试题(已下线)江西省上饶市2023届高三第一次高考模拟考试数学(理)试题变式题16-20(已下线)3.4.3用向量方法研究立体几何中的度量关系(第1课时 夹角问题)(同步练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)江苏省南通市如皋市2024届高三下学期2月诊断测试数学试题
2022·全国·模拟预测
名校
9 . 如图1,在平面四边形
中,已知
,
,
,
,
,
于点
.将
沿
折起使得
平面
,如图2,设
(
).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/8df9f93a-285a-44d5-81bf-e1c7e9596a20.png?resizew=289)
(1)若
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
平面
;
(2)若直线
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864c21e9664fa9111ede6425b09563a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da48240e7fc3248f773ac1500c15ec14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71f070c1aa967a945113735322fae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9295bfd1b7085a86d874617d5f87f099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6be8ab51eec310bfd7d6c01cc311c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/94bd29473c0065517b9427d0147d1c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3ede869e508a8c8bda34a16782f863.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/8df9f93a-285a-44d5-81bf-e1c7e9596a20.png?resizew=289)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
10 . 在几何体
中,底面
是边长为6的正方形,
,
,
,
均为正三角形,且它们所在的平面都与平面
垂直.
是线段
上的动点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/12e03020-2ad4-4276-97df-0cb1f1bf54cf.png?resizew=155)
(1)若
,求三棱锥
的体积;
(2)若平面
平面
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a0c85deb80d8e63bc60127e803f7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ab8de2231d3bfbd289dcdf6d512667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801e866d3f9f26886e271708a73a6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e6648c9e56d68506017df7424be99c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/12e03020-2ad4-4276-97df-0cb1f1bf54cf.png?resizew=155)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1234a7bbfe925eeea7f17d30bfab88b3.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbfb8a8a4d0731f5b237d5c8e169725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fac8b38a9cf7602391f6d6ca933bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-12-04更新
|
472次组卷
|
4卷引用:新疆生产建设兵团地州学校2023届高三上学期一轮期中调研考试数学(理)试题