名校
解题方法
1 . 已知向量
,且
平面
平面
,若平面
与平面
的夹角的余弦值为
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c548218e603eb4464bdd1fe4e5bf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a149e3fbd368c1852d64585e2334a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed43e58b898d683085e39daa0ca7e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() | C.-1或2 | D.![]() |
您最近一年使用:0次
2024-06-10更新
|
175次组卷
|
3卷引用:贵州省六盘水市盘州市第一中学2023-2024学年高二上学期期末考试数学试题
解题方法
2 . 在正方体
中,
是线段
上一点,则
的大小可以为( )
![](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/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6913da03b6e87d163d17c1dc34295c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 正四棱锥
的底面
是边长为6的正方形,高为4,点
,
分别在线段
,
上,且
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/f1ced229-777b-4a22-9abb-d5802d635b43.png?resizew=183)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90dd873422a87e6509a30c94ffdc23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc90576a513851cf09cc257d588c1d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/f1ced229-777b-4a22-9abb-d5802d635b43.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137fcdac119eff6ac5990b6d201615df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
您最近一年使用:0次
4 . 图1是直角梯形
,
,
,
,
,
,
在线段
上,且
,以
为折痕将
折起,使点
到达
的位置,且
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a63bd07c-aa38-4ebd-bc44-753a89833533.png?resizew=326)
(1)求证:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
(2)在棱
上存在点
,使得锐二面角
的大小为
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a14895e4d42943e5a87ba078dd8268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2feceb4322d1f4627e0558c1a81743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9723635d46664a92d3af26362dfea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c8e857d113bd838fed693e584707a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297f713ddbcc4578e73c8afe3a52abfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9b02a4ece39842989088e56b1d988b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/a63bd07c-aa38-4ebd-bc44-753a89833533.png?resizew=326)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570723ec1803bb3a69f220ad7df50226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f615c1e601990cde607f0216f715d57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
2024-01-30更新
|
1370次组卷
|
3卷引用:黑龙江省齐齐哈尔市2023-2024学年高二上学期期末考试数学试题
2024·全国·模拟预测
解题方法
5 . 如图①,在直角梯形
中,
,
,
,
,
,
,
分别在边
上,四边形
为正方形,将
沿着边
旋转,使得
,如图②.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/20bf03eb-c5aa-47b8-af18-42755b8c370e.png?resizew=330)
(1)求证:
平面
;
(2)
是棱
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9186e4574ffe28e673724fcb019db208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424269ceef173843aae76e39ecdf6111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33804bda15aa245e3a64dcc2e4c0b24f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bb57534d77c2355aef18c9105c189d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d8b64ae5ebb831b1d03316e89f4aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3af5833b0cab2dff3e615c8790ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a618e2fa885d453e050c21bc05f8fed4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/20bf03eb-c5aa-47b8-af18-42755b8c370e.png?resizew=330)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ab0137fe07fc29af8eae62bb8a8495.png)
您最近一年使用:0次
解题方法
6 . 直三棱柱
中,点M、N分别为
、
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/d54d7929-e2d3-471a-a482-d508a9e1ce6c.png?resizew=162)
(1)求证:
平面
;
(2)已知
,
,
.
(ⅰ)求直线
与平面
所成角的正弦值;
(ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/d54d7929-e2d3-471a-a482-d508a9e1ce6c.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df209c58c4cc146ef62100e6d3b068d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
(ⅰ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
解题方法
7 . 如图,在直三棱柱
中,底面
是以
为底边的等腰直角三角形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/e6477e84-b721-4bea-b997-1ea2078ae8c8.png?resizew=156)
(1)求证:平面
平面
;
(2)设点
为
上一点,且满足
,求二面角
的平面角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/e6477e84-b721-4bea-b997-1ea2078ae8c8.png?resizew=156)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10e5804cf75c81c4825e8fc408adb4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
您最近一年使用:0次
名校
解题方法
8 . 空间直角坐标系
中,经过点
且法向量为
的平面方程为
,经过点
且一个方向向量为
的直线l的方程为
,阅读上面的材料并解决下列问题:现给出平面α的方程为
,经过点
的直线l的方程为
,则直线l与平面α所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf95be25d34a7366bf4060d081329c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4ac7c3e4d50ea4683f54f80f23ffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff4c767999174c06cee1c45b8fa908d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f353152c7f589c0caf5f964f803ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181d60545ee1d7000e1138709be1b4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b335c281e58bcfc69ed9e9feea4420a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbbfd8b995cf3ad0cb7667f4419ddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b760ad4c3ac6422cc6f771093ec8ffbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b1e0c3fcb578008f60e4892db10260.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-25更新
|
418次组卷
|
2卷引用:四川省成都市西北中学2023-2024学年高二上学期12月阶段性检测数学试题
9 . 如图,在直三棱柱
中,
,
是
的中点.
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c278dc7c5f492954519191fc6726ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9e5564c2aaec71208bda411fd8076b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c7c9b452fba2c98370cd2cf692aceb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2023-12-21更新
|
551次组卷
|
3卷引用:河北省沧州市泊头市2024届高三上学期12月联考数学试题
名校
解题方法
10 . 如图,在三棱台
中,若
平面
,
,
,
,
为
中点,则二面角
的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260ee90b4107dcdc5b2b0937c40e8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e17995e2f71e297d94ae51c7e5b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7abc9839172e487277e8105ad4cd4b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-08更新
|
313次组卷
|
3卷引用:广东省深圳市五校联考2023-2024学年高二上学期12月段考数学试题