2023高二·全国·专题练习
1 . 已知等腰直角
的三个顶点在球O的表面上,且
,连接CO并延长交球O的表面于点D,连接DA,DB;若球O的体积为288π,则直线AC,BD所成角的正切值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4184d0d1b8b79f6f268b7c86e7fda1.png)
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2 . 如图,两条异面直线
所成的角为
,在直线
上分别取点
和点
,使
,且
(
称为异面直线
的公垂线).已知,
,
,则公垂线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51d7fc14599a657b4831a4943360451.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a64340f774b250e6d42d9dc1b127418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8348c89c6f13053325f4e1c62e29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8df14d11c6f036b3b248544b731ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd72669c08e98a92cdfb9bc167ac56bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b0e4666223cd9ab719a5c36ce32e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7c422a19b68b8b4cd484d22897e3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51d7fc14599a657b4831a4943360451.png)
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3 . 如图,异面直线l,m,
,
,
,
,
,
,且
,
,
,
,则异面直线l,m夹角的余弦值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30262f17d1e521b48d773da22ebf452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b76843381162198a14f2faf5e2518b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b043bec560739731fb414fdc47da2ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bba07568684a409eaa92e02e0a3829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b9d83969b6a8e27e57ab71b34e2b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c50360563e2a58800af3a9cf7d9652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0ace693aa9871000cceea36255fe0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73ff3a6a73403c2a25c0d798bb22a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7302e4f0bb743b611015615376d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c559671a60d864715ed73729020f0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/e79e941d-73dd-4db5-b2e9-481fc985eed9.png?resizew=140)
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4 . 已知圆柱
的底面半径和母线长均为
,
,
分别为圆
、圆
上的点,若
,则异面直线
,
所成的角为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca1d1079fc3ac3e8d44159329865cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d85623f82c7d166bc6ae6b403cb5b80.png)
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5 . 在正方体
中,异面直线
与
所成角的大小是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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2023-09-23更新
|
209次组卷
|
3卷引用:专题训练:空间线线角、线面角、面面角求解精练30题-同步题型分类归纳讲与练(人教A版2019必修第二册)
(已下线)专题训练:空间线线角、线面角、面面角求解精练30题-同步题型分类归纳讲与练(人教A版2019必修第二册)河南市柘城县德盛高级中学2022-2023学年高一下学期5月月考数学试题上海市黄浦区向明中学2023-2024学年高二上学期期中数学试题
名校
解题方法
6 . 如图,矩形中,
,M为BC的中点,将
沿直线
翻折,构成四棱锥
,N为
的中点,则在翻折过程中,
①对于任意一个位置总有平面
;
②存在某个位置,使得;
③存在某个位置,使得;
上面说法中所有错误的序号是
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7 . 在三棱锥
中,已知
是边长为
的正三角形,
平面
,
、
分别是
、
的中点,若异面直线
、
所成角的余弦值为
,则
的长为______ ,三棱锥
的外接球表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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解题方法
8 . 已知正四面体ABCD,点E为棱AD的中点,O为
的中心,则异面直线EO与CD所成的角等于_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
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9 . 如图所示,已知正方体
的棱长为1,点E,F分别是棱
的中点,点P是侧面
内一点(含边界).若
平面
,则下列说法正确的有______ .
的轨迹为一条线段
②三棱锥
的体积为定值
③
的取值范围是
④直线
与
所成角的余弦值的最小值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4f409aa1d8abb7fe8d781c3951de02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0875cc63101ea9c8a7ad19a94bd6d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da0522dd9378bab25de2f560aec563.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90357ba810502b61cb8b480701826f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dbb658674a3b07161de9acd1d28a77.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
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解题方法
10 . 在正方体
中,直线
与
所成角大小为________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
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