1 . 如图,在棱长为2的正方体
中,为
棱
的中点,
为棱
的中点,平面
与平面
将该正方体截成三个多面体,其中
,
分别在棱
,
上.
平面
;
(2)求异面直线
与
所成角的余弦值;
(3)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea5787b53322bbfd5a6300aac1b84c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311e9cc12153a72e0b5c9290204badff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8b96bc1fed9c66ef8ab465d7e5362c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311e9cc12153a72e0b5c9290204badff.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb837e11438f2cede53982203c4bd08.png)
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2024-06-08更新
|
557次组卷
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4卷引用:福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题
福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题(已下线)第六章:立体几何初步章末综合检测卷(新题型)-【帮课堂】(北师大版2019必修第二册)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)
解题方法
2 . 如图,在正方体
中,
平面
;
(2)求直线
所成的角的大小;
(3)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756d4d8a7051af5dae3ef56cb9e47c5b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d94b262d997aa1b7b8a807cea2ee17f.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231673dd67ab79d3c5da73904ceade1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756d4d8a7051af5dae3ef56cb9e47c5b.png)
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解题方法
3 . 在直角梯形ABCD中,
,
(如图1),把△ABD沿BD翻折,使得
平面BCD,连接AC,M,N分别是BD和BC中点(如图2).
平面AMN;
(2)记二面角A—BC—D的平面角为θ,当平面BCD⊥平面ABD时,求tanθ的值;
(3)若P、Q分别为线段AB与DN上一点,使得
(如图3),令PQ与BD和AN所成的角分别为
和
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d660e4c409a468277c7892bb44f0aaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77745febf133c1922bffdb8b2a427b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
(2)记二面角A—BC—D的平面角为θ,当平面BCD⊥平面ABD时,求tanθ的值;
(3)若P、Q分别为线段AB与DN上一点,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fea3a02f5849a42fa0317b5091563c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d42cd1f65b49da85d8563e1dca540d4.png)
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解题方法
4 . 如图1,四边形ABCD为菱形,
是边长为2的等边三角形,点M为AB的中点,将
沿AB边折起,使
,连接PD,如图2,
(1)证明:
;
(2)求异面直线BD与PC所成角的余弦值;
(3)在线段PD上是否存在点N,使得
∥平面MCN﹖若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48fdf50d5a0cbd38ee28c89c3509e7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/22/abe6d96b-b9d9-46f5-86c8-dc7d9fffdd23.png?resizew=360)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)求异面直线BD与PC所成角的余弦值;
(3)在线段PD上是否存在点N,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ef4b561b7b521d54540c48f859f5f5.png)
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5 . 已知等边三角形
的边长为4,D为
的中点,将
沿
折到
,使得
为等边三角形,则直线
与
所成的角的余弦值( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/8/dd7cae0f-d575-49cf-b5a2-3b6ad40d4b31.png?resizew=148)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f517953a21c2a45fd8465072c44bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaae2200917767407571ef4980c64afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b32b0bbdc46391dab9533f08f2517a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/8/dd7cae0f-d575-49cf-b5a2-3b6ad40d4b31.png?resizew=148)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 在棱长为1的正方体
中,
分别为棱
的中点,则BE与DF所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570661f3cd27119447394748b3bae6bd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 正方体
中,
,
是
的中点,下列说法中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.过![]() ![]() ![]() ![]() ![]() |
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2023-12-24更新
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634次组卷
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4卷引用:福建省三明市尤溪县第七中学2023-2024学年高一下学期期中考试数学试题
8 . 在长方体
中,已知
,点E是线段CD的中点,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/8171717b85439b483e7985dddbd57966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-20更新
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3卷引用:福建省部分校2024届高三上学期期中考试数学试题
9 . 在正四面体
中,棱长为2,且
是棱
中点,则异面直线
与
夹角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-17更新
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7卷引用:福建省莆田第五中学2023-2024学年高一下学期期中考试数学试卷
福建省莆田第五中学2023-2024学年高一下学期期中考试数学试卷湖北省鄂西北六校(曾都区第一中学等)2023-2024学年高二上学期期中联考数学试题重庆市荣昌中学校2023-2024学年高一下学期4月期中考试数学试题(已下线)第三篇 努力 “争取”考点 专题6 空间角与距离【练】(已下线)专题09 立体几何(5大易错点分析+解题模板+举一反三+易错题通关)-2(已下线)第八章 立体几何初步 单元复习提升(易错与拓展)(1)-单元速记·巧练(人教A版2019必修第二册)(已下线)第八章:立体几何初步章末重点题型复习(2)-同步精品课堂(人教A版2019必修第二册)
10 . 如图,在正方体
中,M是
的中点,则异面直线
,
所成角的余弦值是( )
![](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/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/aec96baf-29ea-4d63-b6bf-e9b59f93cf70.png?resizew=176)
A.![]() | B.![]() | C.![]() | D.![]() |
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