2024·全国·模拟预测
解题方法
1 . 如图,已知长方体
中,
,
,
为正方形
的中心点,将长方体
绕直线
进行旋转.若平面
满足直线
与
所成的角为
,直线
,则旋转的过程中,直线
与
夹角的正弦值的最小值为( )(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67d8576417f761dd5f583ad3a1555a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142e0f0e25dc2ad81ec1a7ec6ed866b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142e0f0e25dc2ad81ec1a7ec6ed866b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903c1bb6f9fe8f9b9710683a3e601452.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bda192938e6048ac769bad63a27aaf2.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知
分别是圆柱
上、下底面圆的圆心,
分别是上、下底面圆周上一点,若
,且直线
与
垂直,则直线
与
所成的角的正切值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c8e67ae6659fb77dc4e33154e4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02bea5e9441f29e640664c0e68c1788b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd37244e07a7f1e6b0d8afdb469cf76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
3 . 《九章算术・商功》刘徽注:“邪解立方得二堑堵,邪解堑堵,其一为阳马,其一为鳖臑,”阳马,是底面为长方形或正方形,有一条侧棱垂直底面的四棱锥.在
底面
,且底面
为正方形的阳马中,若
,则( )
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7831ce178516de8ce45b05dd6401e6.png)
A.直线![]() ![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.四棱锥![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
4 . 卡夫拉金字塔(如图1)由埃及第四王朝法老卡夫拉建造,可通往另一座河谷的神庙和狮身人面像,是世界上最紧密的建筑.从外侧看,金字塔的形状可以抽象成一个正四棱锥(如图2),其中
,点
为
的中点,则
,
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/4/e322b2dc-ce4a-4ebb-8323-b75bad9d3cfb.png?resizew=400)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e9255236684f5ba6e03d5043b815ba.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-05-03更新
|
895次组卷
|
4卷引用:海南省海口市等4地、乐东黎族自治县乐东中学等2校2023届高三高考全真模拟(三)数学试题
海南省海口市等4地、乐东黎族自治县乐东中学等2校2023届高三高考全真模拟(三)数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点2 异面直线所成角综合训练【基础版】江苏省徐州市沛县2022-2023学年高一下学期第二次学情调研数学试题广东省东莞市第一中学2022-2023学年高一下学期期中考试数学试题
5 . 如图,在直角梯形
中,
,D为
边中点,将
沿
边折到
.连接
得到四棱锥
,记二面角
的平面角为
,下列说法中错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/18/ed78f911-cb80-4467-bd91-6010f89b329a.png?resizew=350)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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A.若![]() ![]() ![]() |
B.无论![]() ![]() ![]() |
C.无论![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-03-16更新
|
550次组卷
|
2卷引用:四川省凉山州2023届高三下学期二诊理科数学试题
6 . 安徽徽州古城与四川阆中古城、山西平遥古城、云南丽江古城被称为中国四大古城.徽州古城中有一古建筑,其底层部分可近似看作一个正方体
.已知该正方体中,点
分别是棱
的中点,过
三点的平面与平面
的交线为
,则直线
与直线
所成角为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/a7797eeb-7724-4d1a-a04f-64028d2189d8.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图,三棱锥
中,
是等边三角形,且
,点
在棱
上,点
在棱
上,并使
,其中
,设
为异面直线
与
所成的角,
为异面直线
与
所成的角,则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/f8a2ca72-9801-45fd-9bce-2ceb3f22d9f8.png?resizew=196)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a83ed45064ec6e16c0024adfc8e2804.png)
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A.![]() | B.![]() | C.![]() | D.与![]() |
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2022-11-29更新
|
511次组卷
|
4卷引用:2023年高三数学(理)押题卷五
(已下线)2023年高三数学(理)押题卷五(已下线)第二章 立体几何中的计算 专题一 空间角 微点2 异面直线所成角(二)【培优版】上海市闵行第三中学2022-2023学年高二上学期10月月考数学试题第八章立体几何初步章节验收测评卷-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
解题方法
8 . 手工课可以提高学生的动手能力、反应能力、创造力,使学生在德、智、体、美、劳各方面得到全面发展.某小学生在一次手工课上制作了一座漂亮的房子模型,它可近似地看成是一个直三棱柱和一个长方体的组合图形.其直观图如图所示,
,
,P,Q,M,N分别是棱AB,
,
,
的中点,则异面直线PQ与MN所成角的余弦值是( )
![](https://img.xkw.com/dksih/QBM/2022/6/1/2991817749864448/2996189653639168/STEM/55475cf2-b498-4364-8f4a-42988709fafc.png?resizew=216)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495e21ad0a1bba7716417407ae1523b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab08ad4e668d8c05c3c6333d4f86aae.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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2022-06-07更新
|
527次组卷
|
7卷引用:河南省部分学校2022届高三下学期5月考前最后一卷文科数学试题
河南省部分学校2022届高三下学期5月考前最后一卷文科数学试题河南省部分学校2022届高三下学期5月考前最后一卷理科数学试题(已下线)考向27 空间点、直线、平面之间的位置关系(重点)青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(理)试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点2 异面直线所成角综合训练【基础版】(已下线)8.4.2 空间点、直线、平面之间的位置关系 (精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
解题方法
9 . 已知两平行平面
,
之间的距离为1,
平面
,
平面
,
平面
,
平面
,
,
,则异面直线
与
所成的角的最大值和最小值为( )
![](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/88ff5637d446558d0ca0fcfe3ebd17ea.png)
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A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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10 . 莆田妈祖城有一钟楼,其顶部可视为正四棱柱与正四棱锥的组合体,如图,四个大钟分布在正四棱柱的四个侧面,则每天0点至12点(包含0点,不含12点)相邻两钟面上的时针成60°角的次数是( )
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927703236222976/2932364308193280/STEM/a17efbdac0d54b4d96738f26395999ec.png?resizew=112)
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927703236222976/2932364308193280/STEM/a17efbdac0d54b4d96738f26395999ec.png?resizew=112)
A.2 | B.4 | C.6 | D.8 |
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2022-03-09更新
|
554次组卷
|
4卷引用:福建省莆田市2022届高三3月第二次教学质量检测数学试题
福建省莆田市2022届高三3月第二次教学质量检测数学试题(已下线)押新高考第12题 立体几何-备战2022年高考数学临考题号押题(新高考专用)(已下线)第23练 空间点、直线、平面之间的位置关系福建省泉州市两校2021-2022学年高二下学期期中联考数学试题