1 . 正方体
中,异面直线
与
所成角的大小为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
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2 . 如图所示,圆柱的轴截面
是正方形,E是半圆弧AB的中点,则异面直线
和
所成角的大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/ef530185-a2df-4056-b375-1d7ca8ada86b.png?resizew=150)
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3 . 已知圆台的高为2,上底面圆
的半径为2,下底面圆
的半径为4,
,
两点分别在圆
、圆
上,若向量
与向量
的夹角为60°,则直线
与直线
所成角的大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4f4d4f0fa118f27e890c7940559b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba8f77960739ffbbdec86a9b6685df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
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2024-01-24更新
|
435次组卷
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6卷引用:第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)江苏省苏州市2023-2024学年高二上学期期末学业质量阳光指标调研数学试卷(已下线)模块一 专题6 《空间向量应用》(苏教版)湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题(已下线)专题06 立体几何 第二讲 立体几何中的计算问题(分层练)河南省信阳市新县高级中学2024届高三下学期适应性考试(八)数学试题
4 . 在正方体
中,E为AB的中点,则异面直线
与
所成角为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cf3a313649d7b92f28dd9fb8c27e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
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2024-01-19更新
|
210次组卷
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2卷引用:上海市浦东新区上海海事大学附属北蔡高级中学2023-2024学年高二上学期期末考试数学试题
5 .
是边长为a正方体,
与
所成角的大小______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
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2024-01-16更新
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2卷引用:上海市复旦中学2023-2024学年高二上学期期末考试数学试卷
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6 . 如图,在正四棱柱
中,底面
是正方形,且
,
,经过顶点A和
各作一个平面与平面
平行,前者与平面
交于
,后者与平面
交于
,则异面直线
与
所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2024-01-11更新
|
567次组卷
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6卷引用:上海市徐汇区2023-2024学年高二上学期期末统考数学试卷
上海市徐汇区2023-2024学年高二上学期期末统考数学试卷专题05 空间直线与平面-《期末真题分类汇编》(上海专用)(已下线)第11讲 8.6.1 直线与直线垂直-【帮课堂】(人教A版2019必修第二册)(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(1)-单元速记·巧练(人教A版2019必修第二册)北京市第八十中学2023-2024学年高一下学期期中考试数学试题
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7 . 在正四棱柱
中,
,
,则异面直线
与
所成角的余弦值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e45b0e1c3f6f5bc4cc81290bf263d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
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374次组卷
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3卷引用:上海市向明中学2023-2024学年高二下学期期中考试数学试题
上海市向明中学2023-2024学年高二下学期期中考试数学试题陕西省延安市延川县中学2023-2024学年高一上学期第一次月考数学试题(已下线)专题突破:线线角、线面角、二面角的几何求法盘点-同步题型分类归纳讲与练(人教A版2019必修第二册)
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8 . 如图,在正方体
中,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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/e15b7024-0189-4158-9cbe-907971dc64e3.png?resizew=147)
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9 . 在棱长为
的正方体
中,点
,
,
,
分别为线段
,
,
,
的中点,点
为线段
的动点,则下列说法正确的是___________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/7a010049-e6eb-4642-bce4-aa68a11da773.png?resizew=169)
①异面直线
与
所成角的余弦值为
;②当
为线段
的中点时,点
,
,
,
四点共面:③对任意点的点
,都有平面
平面
;④三棱锥
的外接球的表面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/2024/1/15/7a010049-e6eb-4642-bce4-aa68a11da773.png?resizew=169)
①异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63174f7275c3804fc430c7c36a5ab265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc8dc257bf555c87fd0ad0800e5084b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45160df4f6acbb62c862978ccc779d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3da9085d439248fee8e3ea2d87741a.png)
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解题方法
10 . 在正方体
中,异面直线
与
所成角的大小为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7645d2e05f0e04620075963b715db58.png)
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