名校
解题方法
1 . 如图,已知正三棱柱
的底面边长为1,侧棱
的长为2,E、F分别为
和AC中点,则直线EF与平面
所成角的余弦值为______ ,异面直线
与
所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
您最近一年使用:0次
2 . 如图,在正三棱柱
中,
,
,则直线
与直线
所成角的正切值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在正方体
中,
是
的中点,求
与
两条异面直线所成角的正弦值为________
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在正方体
中,
分别为
和
的中点,则下列说法正确的序号有______ .
,
,
,
四点共面;②
平面
;③
与
所成角为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369aed2d8309af46ac3eaffb9cce537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508b651e7ee34d9b3ea270996d794ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc3f049152c43dd29b12d0a60aa79f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8263493a370d77a1e6e19f331c970955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
5 . 如图,已知平面
平面
,
,
,
,
,则异面直线
与
所成角的余弦值为______ .
![](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/10de2459bc376f9a3de90f74cc18ca7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397937b9b148896118798d71d8d1d6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8916c5d9ea95fb3f718f0a362231a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
名校
6 . 下列命题正确的是__________ .(填序号)
①若一条直线平行于两个相交平面,则这条直线与这两个平面的交线平行;
②垂直于同一条直线的两直线平行;
③两个平面互相垂直,过一个平面内任意一点作交线的垂线,必垂直与另一个平面;
④过两个点与已知平面的垂直的平面可能不存在;
⑤过两条异面直线外任一点有且只有一条直线与这两条异面直线都垂直;
⑥到一个四面体的四个顶点的距离都相等的平面有7个.
①若一条直线平行于两个相交平面,则这条直线与这两个平面的交线平行;
②垂直于同一条直线的两直线平行;
③两个平面互相垂直,过一个平面内任意一点作交线的垂线,必垂直与另一个平面;
④过两个点与已知平面的垂直的平面可能不存在;
⑤过两条异面直线外任一点有且只有一条直线与这两条异面直线都垂直;
⑥到一个四面体的四个顶点的距离都相等的平面有7个.
您最近一年使用:0次
7 . 如图所示,在正方体
中,
与
所成的角为________ ,
与
所成的角为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
您最近一年使用:0次
2024高一下·全国·专题练习
解题方法
8 . 正方体
的棱长为4,点P是棱
上一点(不包括端点),若异面直线
与
所成角的余弦值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9985eaef9e31b243d5aaf89b71f66075.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc89db314967533d44447ea0e0d775ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9985eaef9e31b243d5aaf89b71f66075.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在三棱锥
中,
,点
在棱
上,点
在棱
上,且
,设
表示
与
所成的角,
表示
与
所成的角,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1427dca0e261319dbd9890442122db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
您最近一年使用:0次
2024高一下·全国·专题练习
解题方法
10 . 如图,已知
是圆柱下底面圆的圆心,
为圆柱的一条母线,
为圆柱下底面圆周上一点,
,
,
为等腰直角三角形,则异面直线
与
所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed367b88668d973e54bbae632e92c628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7263feb47362ab697f972d6571ff6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc526324e78e4d9226d1b537f27845a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次