解题方法
1 . 如图,正方体的棱长为1,线段
上有两个动点
,且
,则下列结论中正确的是( )
A.![]() | B.![]() ![]() |
C.异面直线![]() | D.直线![]() ![]() |
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2 . 如图,在三棱锥
中,
,平面
平面
是
的中点,
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/5167ebe6-366d-4bf3-98a9-9fed6659a4f6.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae2e95b42870df8c84d3831467045f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6073645d6b32ffd02450369e203ade0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bef5d4132e7840cd06f6314a8c233e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/5167ebe6-366d-4bf3-98a9-9fed6659a4f6.png?resizew=145)
A.三棱锥![]() ![]() |
B.![]() ![]() ![]() |
C.![]() |
D.三棱锥![]() ![]() |
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3 . 在棱长为2的正方体
中,
在线段
上运动(包括端点),下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.存在点![]() ![]() ![]() |
B.不存在点![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.以![]() ![]() ![]() ![]() |
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632次组卷
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4卷引用:江苏省镇江市扬中市第二高级中学2023-2024学年高三下学期期初检测数学试题
江苏省镇江市扬中市第二高级中学2023-2024学年高三下学期期初检测数学试题福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷江苏省常州市2023-2024学年高三上学期期末学业水平监测数学试卷(已下线)专题06 立体几何 第二讲 立体几何中的计算问题(解密讲义)
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4 . 如图,在三棱柱
中,
在底面ABC上的射影为线段BC的中点,M为线段
的中点,且
,
.
的体积;
(2)求MC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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8431a9f76fe9f867b50a818e8b1cf6c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4475e0a3df7ba0a5679c5f1795525713.png)
(2)求MC与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd544dfc0e7c893a15e2cc23177be184.png)
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2024-03-06更新
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7卷引用:山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题
山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题2024届江苏省南通市徐州市高三2月大联考模拟预测数学试题(已下线)第3讲:立体几何中的探究问题【讲】(已下线)第06讲 空间直线﹑平面的垂直(一)-《知识解读·题型专练》(已下线)高一下学期期中复习解答题压轴题十八大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)第13章 立体几何初步 章末题型归纳总结 (1)-【帮课堂】(苏教版2019必修第二册)(已下线)重难点专题13 轻松搞定线面角问题-【帮课堂】(苏教版2019必修第二册)
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5 . 如图,三棱柱
中,四边形
均为正方形,
分别是棱
的中点,
为
上一点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
平面
;
(2)若
,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/a92e457c6aa0dd5fe8976dc77cae7f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da62d9c339d604c5ffafc82fc54e2b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e516121599c9fcc528121c00afcf52fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cd89328daccadf245e5181b0f03ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
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2024-03-04更新
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1885次组卷
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5卷引用:山东省菏泽第一中学南京路校区2024届高三下学期开学考试数学试题
6 . 已知四棱锥
平面
,四边形
为梯形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2d52f4ca-5838-4f23-a9ee-88d062a9e3b3.png?resizew=163)
(1)证明:平面
平面
;
(2)平面
与平面
的交线为
,求直线
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cd31c659a01b64c1a241c81815c044.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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91aacd63ffc1940a821b955ffb7ae03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/2d52f4ca-5838-4f23-a9ee-88d062a9e3b3.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b60870baa5e3fbc33a749aa5f0a94be.png)
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7 . 如图所示,在长方体
中,
,
,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/4142252d-d59c-4ad3-9e16-9878b36dcc3b.png?resizew=115)
(1)求异面直线
和
所成的角的正切值;
(2)求
与平面
所成的角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66200ae44919a57caf401a6d47737ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd34ae1a0406994d2c07a61e9220a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094e639c2b31dc54b1b3e6456e77843.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/4142252d-d59c-4ad3-9e16-9878b36dcc3b.png?resizew=115)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3640223cc216227526e79e487aea89b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa62b5a161c20430cb1dda9809247f3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0e65e147b109f2bbfd3a3f502bbc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8effc47b601f75015bf109caa8dc559.png)
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8 . 如图,已知正方形
的边长为1,
平面
,三角形
是等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/8f4f328a-c6c2-4307-b12b-86ff4e7c7d22.png?resizew=143)
(1)求异面直线
与
所成的角的大小;
(2)点
在线段
上,若
,求
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dba76518a473722e04cfbac3a4333bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dba76518a473722e04cfbac3a4333bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/8f4f328a-c6c2-4307-b12b-86ff4e7c7d22.png?resizew=143)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348fb71fbc47fd87e9ce011652ef4186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
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解题方法
9 . 已知圆锥的顶点为
,底面圆心为
,
为底面直径,
,
,点
在底面圆周上,且点
到平面
的距离为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/f8b3bfde4b7cbca10de7d63bb7b2cfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
A.该圆锥的体积为![]() | B.直线![]() ![]() ![]() |
C.二面角![]() ![]() | D.直线![]() ![]() ![]() |
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2024-02-05更新
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4卷引用:河南省郑州市宇华实验学校2023-2024学年高二下学期开学摸底考试数学试题
河南省郑州市宇华实验学校2023-2024学年高二下学期开学摸底考试数学试题山东省威海市2023-2024学年高二上学期期末考试数学试题(已下线)专题08 立体几何异面直线所成角、线面角、面面角及平行和垂直的证明 -《期末真题分类汇编》(北师大版(2019))(已下线)高一数学期末模拟试卷02-《期末真题分类汇编》(北师大版(2019))
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解题方法
10 . 如图,在多面体
中,四边形
为平行四边形,且
平面
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49adfc06a83004ec42a22d9a06c26af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
.点
分别为线段
上的动点,满足
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
平面
;
(2)是否存在
,使得直线
与平面
所成角的正弦值为
?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1caf5676a9bb01365907b62af59fdbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49adfc06a83004ec42a22d9a06c26af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4b833fb7dd03c34ac40c664cd8483d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2be5f930744983e6829e8c06dc3204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4649d20f21891975c52cc85dabd83622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2e3526bc8be03b7a602d25ea2c7e24.png)
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2024-01-31更新
|
1370次组卷
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6卷引用:四川省成都市第七中学2023 2024学年高三下学期入学考试理科数学试卷
四川省成都市第七中学2023 2024学年高三下学期入学考试理科数学试卷四川省成都市第七中学2024届高三下学期开学考试数学(理)试题浙江省湖州市2024届高三上学期期末数学试题湖南省2024届高三数学新改革提高训练二(九省联考题型)(已下线)黄金卷03(2024新题型)(已下线)高二数学下学期期末押题试卷02(测试范围:新高考全部内容)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)