名校
1 . 如图,在四面体
中,底面ABC是边长为1的正三角形,
,点P在底面ABC上的射影为H,
,二面角
的正切值为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/b163ccc3-5d33-4632-973d-143b3937f0da.png?resizew=146)
(1)求证:
;
(2)求异面直线PC与AB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d975f472e1663622e2b7629a3f5ff95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97145e11dfb0e127164187f11288e6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f7a0ab16cbb95691b3d80334a91401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/b163ccc3-5d33-4632-973d-143b3937f0da.png?resizew=146)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
(2)求异面直线PC与AB所成角的余弦值.
您最近一年使用:0次
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2 . 如图,在正三棱柱
中,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/c52e064b-a853-4880-bd60-f694520b0464.png?resizew=148)
(1)证明:
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/c52e064b-a853-4880-bd60-f694520b0464.png?resizew=148)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b0bfe1e7a956345f7ed58a3b2faa70.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
2023-12-26更新
|
416次组卷
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3卷引用:河南省周口市项城市5校2024届高三上学期11月联考数学试题
3 . 如图所示,已知四棱锥
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f46fc4f2-dc7b-4ace-8501-d03e7b61912d.png?resizew=171)
(1)求证:
平面
;
(2)当四棱锥
的体积最大时,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939f353a411d07176c1e2c064ef07322.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/f46fc4f2-dc7b-4ace-8501-d03e7b61912d.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
您最近一年使用:0次
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解题方法
4 . 如图,在三棱锥
中,
分别是线段
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/8d49c433-aa50-44ba-ba77-74a1d6696682.png?resizew=131)
(1)求证:
平面
;
(2)若二面角
的余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfa997d03be071dcd31893c67346be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b691cf4f8fb736448e10447184e6de3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fab8809915a89426395187aca7af02a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/8d49c433-aa50-44ba-ba77-74a1d6696682.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea10539215794cd76e8b211abd503f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
您最近一年使用:0次
2023-12-13更新
|
782次组卷
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5卷引用:河南省周口市项城市五校2024届高三上学期12月联考数学试题
名校
5 . 如因,直线
垂直于圆
所在的平面,
内接于圆
,且
为圆
的直径,
,
,则三棱锥
的外接球的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e5a8fdbfbdf25f6937b7a2d6a4cd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/c91080fc-35ea-4012-b1d2-7120ccb7711a.png?resizew=146)
您最近一年使用:0次
2023-11-25更新
|
161次组卷
|
2卷引用:河南省周口市项城市5校2024届高三上学期11月联考数学试题
解题方法
6 . 如图,在四棱锥
中,底面ABCD为菱形,
平面ABCD,
,
,
,E是BC的中点.
(1)证明:
;
(2)若线段PD上存在一点H满足
,使得
,求λ的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/43483013-850c-45e0-998b-6f1dc0f78e47.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304e9d63e7fdc531f4f7b805b765a1b1.png)
(2)若线段PD上存在一点H满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affa607ce5285c24cbfc40ef49b4f4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187f43e7f2f0f91a74a07169e1acaf6d.png)
您最近一年使用:0次
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7 . 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
|
1688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
8 . 如图,在四棱锥
中,底面ABCD是平行四边形,
,
平面ABCD,
,
,F是BC的中点.
(1)求证:
平面PAC:
(2)试在线段PD上确定一点G,使
平面PAF,请指出点G在PD上的位置,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd893c4964b7f1ef69f0563d74c76d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/12/82d9e6c1-0241-4a8d-ae39-52f650551a66.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
(2)试在线段PD上确定一点G,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48f3a086c6961c5ba7e121a4e60738e.png)
您最近一年使用:0次
9 . 已知
是球O的直径,
,C,D是球面上两点,
,
,
与平面
所成的角为
,则四面体
的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
10 . 在三棱台
中,
平面
,
,
,
,
.
.
(2)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/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2f39d3fcb1664705228e683c2cc3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2023-07-09更新
|
786次组卷
|
9卷引用:河南省周口市2022-2023学年高一下学期期末数学试题
河南省周口市2022-2023学年高一下学期期末数学试题河北省邢台市2022-2023学年高一下学期期末数学试题(已下线)第一章 空间向量与立体几何 章末测试(基础)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)湖南省名校联盟2023-2024学年高二上学期入学摸底考试数学试题新疆石河子第一中学2023-2024学年高二上学期9月月考数学试题重庆市第七中学校2023-2024学年高二上学期期末模拟检测数学试题(已下线)8.6.1直线与直线垂直+8.6.2直线与平面垂直——课后作业(提升版)(已下线)重组1 高一期末真题重组卷(河北卷)B提升卷福建省泉州市安溪第一中学2023-2024学年高一下学期6月份质量检测数学试题