1 . 已知直三棱柱
的各棱长均相等,体积为
,
为
中点,则点
到平面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-09-11更新
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8卷引用:福建省福州外国语学校2022-2023学年高一下学期期末质量检测数学试题
福建省福州外国语学校2022-2023学年高一下学期期末质量检测数学试题天津市四校联考2020-2021学年高一下学期期末数学试题河北省石家庄市二十七中2021-2022学年高二上学期第一次月考(10月)数学试题上海市松江二中2021-2022学年高二上学期期中数学试题海南华侨中学2021-2022学年高二上学期第二次段考数学试题(已下线)第11讲 柱、锥、台的体积(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)(已下线)期中模拟预测卷01(测试范围:空间向量与立体几何、数列) -2022-2023学年高二数学上学期期中期末考点大串讲(沪教版2020必修第三册+选修一)上海市嘉定区封浜高级中学2022-2023学年高二上学期11月期中数学试题
名校
解题方法
2 . 在棱长为1的正方体
中,点
,
分别满足
,
,其中
,
,则( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f322f8f148fbbaa38b6c0218ae68fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba4237e3605176f48bd10d08f5edf5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7e13498fcf482fb92fe0b84801fe52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
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7卷引用:福建省厦门市2020-2021学年高二下学期期末数学试题
福建省厦门市2020-2021学年高二下学期期末数学试题江苏省苏州市昆山市周市高级中学2021-2022学年高三上学期暑期网课自主学习测试数学试题广东省中山市华侨中学2021-2022学年高二上学期第一次段考数学试题(已下线)2022届高三普通高等学校招生全国统一考试数学信息卷(四)(已下线)第08讲 空间向量的应用-【寒假自学课】2022年高二数学寒假精品课(苏教版2019选择性必修第二册)(已下线)2022年新高考模拟卷(一)-2022年高考数学【热点·重点·难点】专练(新高考专用)河北省百师联盟2024届高三上学期开学考试数学试题
解题方法
3 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,
为线段
的中点,
为线段
上的动点.
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758143769706496/2779884915458048/STEM/e255c8d0173f4bfdae48084dded2a7e5.png?resizew=168)
(1)若平面
交
于点
,求证:
;
(2)求证:
平面
;
(3)判断直线
与平面
所成角的大小是否可以为
,并说明理由.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758143769706496/2779884915458048/STEM/e255c8d0173f4bfdae48084dded2a7e5.png?resizew=168)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc143c7fd7c471ca91b6ccc22438fdd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
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2021-08-05更新
|
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2卷引用:福建省福州市四校联盟2021-2022学年高一下学期期末联考数学试题
4 . 如图,四棱锥
中,平面
平面
,
,四边形
是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/2c70c328-1683-4c94-9216-b5b1598432e8.png?resizew=165)
(1)直线
与平面
是否垂直?若垂直,请证明;若不垂直,请说明理由;
(2)若二面角
的平面角为60°,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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/2c70c328-1683-4c94-9216-b5b1598432e8.png?resizew=165)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9f756419912dd298a0d6857130c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2021-08-04更新
|
738次组卷
|
2卷引用:福建省厦门市2020-2021学年高一下学期期末数学试题
解题方法
5 . 如图(1)平行六面体容器
盛有高度为
的水,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35eae4a2551fa4504cab9ba04ca737.png)
.固定容器底而一边
于地面上,将容器倾斜到图(2)时,水面恰好过
,
,
,
四点,则
的值为( )
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758350145085440/2778947132727296/STEM/cfc335d7-811e-41ea-beca-141b87f301ed.png?resizew=452)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991451c5002137302527700e195220e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35eae4a2551fa4504cab9ba04ca737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d27f9471b5a5d56e107a7b43f041f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758350145085440/2778947132727296/STEM/cfc335d7-811e-41ea-beca-141b87f301ed.png?resizew=452)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-04更新
|
1232次组卷
|
7卷引用:福建省厦门市2020-2021学年高一下学期期末数学试题
福建省厦门市2020-2021学年高一下学期期末数学试题(已下线)高一数学下学期期末全真模拟卷(3)(必修二全部内容)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)专题23 立体几何中的压轴小题-3(已下线)考向30 线线角、线面角、二面角与距离问题(四大经典题型)(已下线)立体几何专题:空间几何体中的5种距离问题(已下线)专题10 空间角与空间距离的综合(2) - 期中期末考点大串讲(已下线)第四节?直线,平面垂直的判定与性质(讲)
名校
6 . 已知
,
表示两条不同的直线,
,
,
表示三个不同的平面,则下列命题不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
您最近一年使用:0次
2021-08-03更新
|
303次组卷
|
2卷引用:福建省南平市2020-2021学年高一下学期期末数学试题
7 . 如图1,
中,
,
,
,D,E分别是
,
的中点.把
沿
折至
的位置,
平面
,连接
,
,F为线段
的中点,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/72146627-7751-4568-b0ee-c7439c0bc1d4.png?resizew=296)
(1)求证:
平面
;
(2)当三棱锥
的体积为
时,求直线
与
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c72495428bbbd12cad3271b0654ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/72146627-7751-4568-b0ee-c7439c0bc1d4.png?resizew=296)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0bd4b30dc777ac9da80f6baa3eb31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1112ffa328ed486ffc5e4a605eb510e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
名校
8 . 在正四棱柱
中,顶点
到对角线
和到平面
的距离分别为
和
,若侧棱的长大于底面的边长,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363ef68e6d9ad26f50d04d24b8ae07a8.png)
A.![]() | B.![]() |
C.![]() | D.前三个答案都不对 |
您最近一年使用:0次
名校
解题方法
9 . 在正方体
中,
为棱
的中点,则异面直线
与
所成的角为( )
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.90° | B.60° | C.45° | D.30° |
您最近一年使用:0次
名校
解题方法
10 . 正三棱柱
中,
,点
在棱
上,
,则二面角
的正切值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375e3338b7d02d7d315db3a676bdb78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562d1f59ce4a5cf7235ba2c4a01354dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2313ef619728cc5485a687bbb754e.png)
A.![]() | B.![]() | C.![]() | D.3 |
您最近一年使用:0次
2021-07-21更新
|
3913次组卷
|
5卷引用:福建省漳州第一中学2020-2021学年高一下学期数学期末试题