名校
解题方法
1 . 如图,经过边长为1的正方体的三个项点的平面截正方体得到一个正三角形,将这个截面上方部分去掉,得到一个七面体,则这个七面体内部能容纳的最大的球半径是______ .
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2024-04-19更新
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1032次组卷
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6卷引用:江苏省启东中学2023-2024学年高二年级下学期数学第二次月考
江苏省启东中学2023-2024学年高二年级下学期数学第二次月考辽宁省部分学校2024届高三第二次联考(二模)数学试题(已下线)模块4 二模重组卷 第2套 全真模拟卷(已下线)第29题 立体问题常思降维化平面,几何最值莫忘函数不等式(优质好题一题多解)(已下线)专题5 空间向量的应用问题【练】(已下线)宁夏回族自治区银川一中2024届高三下学期第四次模拟考试数学(理)试卷
2 . 如图,四面体
中,
.
(1)求证:平面
平面
;
(2)若
,
①若直线
与平面
所成角为30°,求
的值;
②若
平面
为垂足,直线
与平面
的交点为
.当三棱锥
体积最大时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6c03029467212c952b89696f45456d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/23/2f9a3c3f-41a9-40b4-a456-a8b33158146b.png?resizew=164)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06123e81c41198c76a3335757fac2c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e156c3e4ffa35ed0ac6526c8d8753d.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d742e749b1140b21512408d555f14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be743a99c9d9c2775ced96ccf86d178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f0b8e4d79f6276b0ab054d887183a8.png)
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2024-04-19更新
|
842次组卷
|
4卷引用:江苏省扬州市扬州中学2023-2024学年高二下学期5月月考数学试题
江苏省扬州市扬州中学2023-2024学年高二下学期5月月考数学试题江苏省南京市五所高中学校合作联盟2023-2024学年高二下学期期中学情调研数学试卷(已下线)模块三 专题2 解答题分类练 专题3 空间向量线性运算(苏教版)江苏高二专题02立体几何与空间向量(第二部分)
名校
解题方法
3 . 设三个向量
不共面,那么对任意一个空间向量
,存在唯一的有序实数组
,使得:
成立.我们把
叫做基底,把有序实数组
叫做基底
下向量
的斜坐标.已知三棱锥
.以
为坐标原点,以
为
轴正方向,以
为y轴正方向,以
为
轴正方向,以
同方向上的单位向量
为基底,建立斜坐标系,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb4f795474089c4ca5183f0b8c8210d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977e7b03370104a3b2a99d7b2fc207e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f263fe996c25f0e231e27d2be0262275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82421141d6bb7a2f079659984133fe23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6592338e3a40aeb3f59f6817aad98899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d6c690993b231b20c7a969178e5c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7972794bf959560d01203713beeb5b08.png)
A.![]() | B.![]() ![]() |
C.若![]() ![]() | D.异面直线AP与BC所成角的余弦值为![]() |
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2024-04-01更新
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3卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
4 . 如图所示的六面体中,
,
,
两两垂直,
连线经过三角形
的重心
,且
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07e98f7a65097311e8d93bd9f2af26e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若点![]() ![]() ![]() |
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2023-12-20更新
|
771次组卷
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3卷引用:江苏省苏州市南京师大苏州实验学校2024届高三上学期阶段测试(五)数学试题
名校
解题方法
5 . 已知正方体
的棱长为
为底面
、
的中心,分别将线段
、
延长距离
到点
和
,依次连接
,
并延长交于点
,顺次连接
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad99659f9ffa4fc2484544b064cf489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.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/6c98b985b0647161a68aa280faac32cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc4d5ff120f751d3645276ed3514929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f3c3818a6aea98356a7f65b955a9b5.png)
A.![]() |
B.平面![]() ![]() |
C.当且仅当![]() ![]() |
D.当![]() ![]() |
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名校
解题方法
6 . 已知图①中四边形
是圆
的内接四边形,沿
将
所在圆面翻折至如图②所示的位置,使得
.
(1)若
,证明:
;
(2)若
,求二面角
余弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212bfbd5575772ca36d6fc3e7b246e49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/7/00bb3173-f178-4afc-a32a-ce9df56155f4.png?resizew=283)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11630c98df712a47b68e9164cc8670d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125525eace86ae47a292f1b5d5b684e2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc87e265613c62406721428c033b77d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
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解题方法
7 . 在矩形
中,
、
分别为
、
上的点,
与
交于点
,
,
,
.将四边形
沿着
翻折成四边形
(
不在平面
内).
(1)若平面
平面
,求棱锥
的体积;
(2)求直线
与平面
所成角的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62bfd459545a3a6d3d442a3b10c85d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70d05c03d14c3bd6f61746e556c1f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/27/5b45cae2-8c70-42f3-851d-3ef0b37b0c6f.png?resizew=377)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bced6a5684b528116e9ce318769a86b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1458c16ce1bc8c84b6112edee3b9e116.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777af29759a4d6c6178843165c2be7ed.png)
您最近一年使用:0次
名校
8 . 下列结论正确的是( )
A.两个不同的平面![]() ![]() ![]() |
B.直线![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2023-03-04更新
|
637次组卷
|
4卷引用:江苏省常州市华罗庚中学2022-2023学年高二下学期3月阶段测试数学试题
名校
解题方法
9 . 六面体
中,底面ABCD、
分别是边长为4和2的正方形,侧面
、侧面
均是直角梯形,且
,
.若该六面体为台体,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/1f3f9023-084d-45ef-a6d4-ce731e52b21b.png?resizew=252)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4efb23bd85a1e3a98c7e7f56a51753f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/28/1f3f9023-084d-45ef-a6d4-ce731e52b21b.png?resizew=252)
A.六面体![]() |
B.异面直线![]() ![]() ![]() |
C.二面角![]() ![]() |
D.设P为上底面上一点,且![]() |
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2023-02-27更新
|
868次组卷
|
3卷引用:江苏省常州市华罗庚中学2022-2023学年高二下学期3月阶段测试数学试题
江苏省常州市华罗庚中学2022-2023学年高二下学期3月阶段测试数学试题江苏省苏州市2022-2023学年高三下学期2月学业质量调研数学试题(已下线)安徽省“江南十校”2023届高三下学期3月一模数学试题变式题6-10
名校
10 . 如图,圆台
的轴截面为等腰梯形
,
,B为底面圆周上异于A,C的点.
内,过
作一条直线与平面
平行,并说明理由;
(2)设平面
∩平面
,
与平面QAC所成角为
,当四棱锥
的体积最大时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c6d80251fdeabfebd65bca460d55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bd886276f8ff9df2a42013b337d726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c6c1f6d821af7e3c8058993218a861.png)
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2023-02-25更新
|
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8卷引用:江苏省连云港市灌南高级中学2022-2023学年高二下学期第二次月考数学试题