1 . 如图,在三棱锥
中,
的中点分别为
.
的长;
(2)证明:平面
平面
;
(3)求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607d2e6bf6337d559bcd3d45f1f45afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630201207817c1b492c50332eabebaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf006d9cf9568dd567c25fd20a0c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
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2024-04-17更新
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2卷引用:内蒙古自治区呼和浩特市第二中学2023-2024学年高二下学期4月月考数学试题
名校
解题方法
2 . 在正方体
中,
分别为棱
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161e7f7142e64070a9fbe0cc907c91c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85328a5b0f25b94b233645df67a95253.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.平面![]() ![]() |
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2024-04-17更新
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2卷引用:内蒙古乌海市第十中学2024届高三下学期4月月考文科(一)数学试题
名校
3 . 如图,已知正三棱柱
分别为棱
的中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08779b8f171e17017a891f876df7fc0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fdf6f784f618a70fb4768f74aa970b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e16f65c3a318220c2f5baac171bbb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14588eb195962ce563e0c7a551510a48.png)
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2024-03-31更新
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3卷引用:内蒙古赤峰市赤峰二中2023-2024学年高二下学期第一次月考数学试题
解题方法
4 . 已知正方体
,且棱长为1,下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() |
C.点![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() |
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名校
解题方法
5 . 如图,在正四棱柱
中,
,
是棱
上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/624d6878-f2ec-47ae-b5dd-235dd5dc4a24.png?resizew=120)
(1)求证:
;
(2)若
是棱
的中点,求异面直线
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/2023/12/20/624d6878-f2ec-47ae-b5dd-235dd5dc4a24.png?resizew=120)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ab924e3692515bd8be4c36472a959a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
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2023-12-19更新
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6卷引用:内蒙古自治区通辽市科尔沁左翼中旗实验高级中学2024届高三上学期12月月考数学(理)试题
内蒙古自治区通辽市科尔沁左翼中旗实验高级中学2024届高三上学期12月月考数学(理)试题四川省遂宁市射洪中学校2023-2024学年高二上学期第三次学月考试数学试题(已下线)艺体生一轮复习 第七章 立体几何 第35讲 空间向量及其运算【讲】(已下线)专题13 空间向量的应用10种常见考法归类(1)(已下线)专题05用空间向量研究距离、夹角问题(2个知识点6种题型1个易错点1种高考考法)(1)(已下线)第6章 空间向量与立体几何 章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)
6 . 如图,
为圆锥的顶点,
是圆锥底面的圆心,
为底面直径,
,
是底面的内接正三角形,
为
上一点.
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/df465d41-3a2c-4b65-9250-c9df47de9f9b.png?resizew=148)
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e50e094cd2849e38859b36aad0b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e8472f8ceb1721ba449151e5aa2c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/df465d41-3a2c-4b65-9250-c9df47de9f9b.png?resizew=148)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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解题方法
7 . 如图所示,若长方体
的底面是边长为2的正方形,高为4,
是
的中点,则下列说法正确的是( )
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/29/6ab4eb93-d6e1-41ba-a637-598e9fe456da.png?resizew=114)
A.点B到直线![]() ![]() |
B.三棱锥![]() ![]() |
C.平面![]() ![]() |
D.三棱锥![]() ![]() |
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2023-11-24更新
|
542次组卷
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2卷引用:内蒙古自治区赤峰市赤峰第四中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
8 . 如图,在矩形
中,
,
,E为线段
中点,现将
沿
折起,使得点D到点P位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/d44a0903-dde4-47fd-ae48-0ecb9544688f.png?resizew=351)
(1)求证:平面
平面
;
(2)已知点M是线段
上的动点(不与点P,C重合),若使平面
与平面
的夹角为
,试确定点M的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12319a1cdcc58d25c30d2b3ab5848237.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/d44a0903-dde4-47fd-ae48-0ecb9544688f.png?resizew=351)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc60341dc04f3fc7133ed29edc6acdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)已知点M是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2e849754baf604fa48efe2c82657af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec7e56107b5f2f34e420caffd1159b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
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2023-11-19更新
|
459次组卷
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2卷引用:内蒙古呼和浩特市内蒙古师范大学附中2023-2024学年高二上学期12月月考数学试题
名校
解题方法
9 . 如图,四棱锥
的底面ABCD是矩形,
平面ABCD,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/ff3f7a21-e910-48a5-9e99-5cd118c72885.png?resizew=139)
(1)求证:
平面
;
(2)求二面角
余弦值的大小;
![](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/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/ff3f7a21-e910-48a5-9e99-5cd118c72885.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9f756419912dd298a0d6857130c80.png)
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2023-10-18更新
|
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6卷引用:内蒙古自治区赤峰市赤峰二中2023-2024学年高二上学期第二次月考数学试题
名校
解题方法
10 . 如图,在四棱锥
中,
为正三角形,底面
为直角梯形,
,
,
,
,
.
(1)求证:平面
平面
;
(2)棱
上是否存在点M,使得二面角
的大小为
,若存在,求出
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18120a244d3a1f9c1688bf53eb2ad775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a0c299356c26338d4153748e8a61d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/2d04226f-2101-42be-aaf8-cd4f75eacc4f.png?resizew=144)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fe44cb45b52ade75574ed31d05fb26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
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2023-10-17更新
|
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