1 . 已知正方体
的棱长为2,点
是
的中点,点
满足
,
,则下列结论正确的是( )
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee2271ff6f44f9a0bd27c3d5cd704e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
A.![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() | D.三棱锥![]() ![]() |
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解题方法
2 . 四面体
中,
,
,
两两互相垂直,且
,
是
的中点,异面直线
与
所成的角的大小为
,求线段
的长______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63594fe6c8fc7b8c28e9cd37aab0dd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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解题方法
3 . 如图,四边形
都是边长为2的正方形,平面
平面
,P,Q分别是线段
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/309ea316-f7fc-42f6-b9ab-a74b376f875a.png?resizew=151)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9f1d8b6eead1dc79af156d6a113431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e88ee337b7c9082f4fe84fd1752d55a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/309ea316-f7fc-42f6-b9ab-a74b376f875a.png?resizew=151)
A.![]() |
B.异面直线![]() ![]() |
C.点P到直线![]() ![]() |
D.![]() ![]() |
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4 . 正方体
中,
分别是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd742708df80435e810a80bf9ec424ab.png)
的中点,则直线
与直线
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11875255224766f69d7fda20c2b12f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52041559f8fee18bfa3e2e2ac07c3bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd742708df80435e810a80bf9ec424ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 如图,两条异面直线
所成的角为
,在直线
上分别取点
和点
,使
.已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68b9de39412963f5f81d1e3e4ff3083.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debaee4d729e1ff6d453ad3f8ef6e61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8348c89c6f13053325f4e1c62e29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4e918c308c88d129c265f0cfc61202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e521cd4cef84c5e7fe395ae5cffa2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68b9de39412963f5f81d1e3e4ff3083.png)
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6 . 在棱长为2的正方体
中,点
,
,
分别是线段
,线段
,线段
上的动点,且
.则下列说法正确的有( )
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771764b4ccfe35b79337f7ce18331c4b.png)
A.![]() |
B.直线![]() ![]() ![]() |
C.三棱锥![]() |
D.当四棱锥![]() ![]() |
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2024-03-07更新
|
1336次组卷
|
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7 . 如图,已知正四棱锥
的所有棱长均为
为棱
的中点,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba964c27f118895f13672321aebe5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-04更新
|
798次组卷
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8卷引用:山东省烟台第一中学2023-2024学年高二下学期2月月考数学试题
山东省烟台第一中学2023-2024学年高二下学期2月月考数学试题(已下线)8.4.2空间点、直线、平面之间的位置关系(第1课时)(已下线)专题13.7空间中的距离和夹角问题-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.3空间点、直线、平面之间的位置关系-【帮课堂】(北师大版2019必修第二册)浙江省杭州市西湖高级中学2023-2024学年高一下学期5月月考数学试题(已下线)重难点专题12 利用几何法求异面直线所成的角-【帮课堂】(苏教版2019必修第二册)(已下线)第十一章:立体几何初步章末重点题型复习(1)-同步精品课堂(人教B版2019必修第四册)山东省德州市夏津育中万隆中英文高级中学2023-2024学年高一下学期5月月考数学试题
名校
解题方法
8 . 如图,在棱长为2的正方体
中,点
是线段
上的动点. 则 ( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/a9f1034f-04e0-4421-af95-e98adaa36653.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3defdd4d0c665d55184b84a7eb316f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/a9f1034f-04e0-4421-af95-e98adaa36653.png?resizew=163)
A.![]() ![]() ![]() | B.![]() |
C.直线![]() ![]() ![]() | D.三棱锥![]() ![]() |
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9 . 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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10 . 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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