23-24高三上·浙江绍兴·期末
解题方法
1 . 如图,三棱柱
是所有棱长均为2的直三棱柱,
分别为棱
和棱
的中点.
面
;
(2)求二面角
的余弦值大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96e23f7b5d3b1dcac47c19fd6da8860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cdf382d6962a5fee6064dcae93e37f.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在棱长为
的正方体
中,
、
分别为
与
的中点.
与
所成的角的余弦值;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2638646f25490fc9b3c7fd05a202128e.png)
您最近一年使用:0次
解题方法
3 . 在长方体
中,
,点
为棱
的中点,则二面角
的大小为__________ .(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed1da7a28fb1983af25f2be2ed03cd3.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/35988677892d6ffdf4773f7a861f26a4.png)
您最近一年使用:0次
名校
解题方法
4 . 已知圆锥的顶点为
,底面圆心为
,半径为2.
,求圆锥的体积;
(2)设
是底面半径,且
是线段
的中点,如图.求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4986217611fc5eefe70fd217a9d5726a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c02fbe7b8bd2331e41f2e7318a751cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b08bdda2ae1bfe83a74c5ee9ca9196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44cd09d9ad46264de4620c60370d49d.png)
您最近一年使用:0次
2023-05-29更新
|
364次组卷
|
3卷引用:上海市青浦区2022-2023学年高二下学期期末数学试题
上海市青浦区2022-2023学年高二下学期期末数学试题上海市交通大学附属中学2023届高三下学期5月卓越考3数学试题(已下线)上海市高二下学期期末真题必刷01(易错题)--高二期末考点大串讲(沪教版2020选修)
5 . 如图,在直三棱柱
中,底面
是等腰直角三角形,
,
为侧棱
的中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb717228e1762d335814a3adc90eae45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecb9a40cfcca4c0ca203b95861e2fdf.png)
您最近一年使用:0次
2023-04-12更新
|
897次组卷
|
5卷引用:上海市青浦区2023届高三二模数学试题
上海市青浦区2023届高三二模数学试题(已下线)专题07 空间向量与立体几何(已下线)2023年北京高考数学真题变式题16-21甘肃省临夏州积石山保安族东乡族撒拉族自治县积石中学2022-2023学年高二下学期期中考试数学试题广东省韶关市新丰县第一中学2022-2023学年高二下学期期中数学试题
名校
解题方法
6 . 四边形
是边长为1的正方形,
与
交于
点,
平面
,且二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/662676a7-4f5f-4e81-ae57-e62a7c32acdc.png?resizew=160)
(1)求点
到平面
的距离;
(2)求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/662676a7-4f5f-4e81-ae57-e62a7c32acdc.png?resizew=160)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-04-06更新
|
713次组卷
|
4卷引用:上海市青浦高级中学2023-2024学年高二上学期12月质量检测数学试卷
名校
解题方法
7 . 已知四面体
的各棱长均为1,D是棱OA的中点,E是棱AB的中点,设
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/19/87ffb349-9c4f-45be-9c94-53d583b6b0cd.png?resizew=187)
(1)用向量
、
、
表示
、
;
(2)判断
与
是否垂直;
(3)求异面直线BD与CE所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211429ce394297f664f6b8e16edec714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2809b448b246cfd11bba7a003c8311.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/19/87ffb349-9c4f-45be-9c94-53d583b6b0cd.png?resizew=187)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781e3daa2c4e018ca0ae09bb56abc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0735144f6e24b6b32028ff14c17c1cec.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781e3daa2c4e018ca0ae09bb56abc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0735144f6e24b6b32028ff14c17c1cec.png)
(3)求异面直线BD与CE所成的角.
您最近一年使用:0次
名校
8 . 如图,在直棱柱
中,
,
,D,E,F分别是
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c5e4e7b8-5d4f-4fa3-8bf9-675045f1e0e6.png?resizew=165)
(1)求证:
;
(2)求
与平面DEF所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bd8c13192ca45c16dad5d59b547220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c5e4e7b8-5d4f-4fa3-8bf9-675045f1e0e6.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe81d0b136fc2acc97ab50ffbf6edf.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2022-11-25更新
|
551次组卷
|
3卷引用:上海市青浦高级中学2024届高三上学期10月质量检测数学试题
名校
9 . 在梯形
中,
,
,
,P为AB的中点,线段AC与DP交于O点(如图1).将
沿AC折起到
位置,使得平面
平面
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7f4fd035-e109-4774-8bba-06663dbfbeae.png?resizew=495)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
平面
;
(2)求二面角
的大小;
(3)线段
上是否存在点Q,使得CQ与平面
所成角的正弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89ee6576c35c682bcb0eff43bd958d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6829c6214e60edbfbf1e31601c6bcb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3c5eea67eecdd13a2e6cd60d1d67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7f4fd035-e109-4774-8bba-06663dbfbeae.png?resizew=495)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde275553b4e49f5adffe606875c6ec3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845b65a3d273b6792d63f3d925cd4bc0.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be451ce5fad246389ccf4864929d81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e95fa1c3bcd3d0464fcadf248e90ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80dbac2006d30c49943f0241fd976eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b188172a322d69106c638e1603ac13f.png)
您最近一年使用:0次
2022-11-08更新
|
558次组卷
|
6卷引用:上海市青浦高级中学2022-2023学年高二上学期12月质量检测数学试题
上海市青浦高级中学2022-2023学年高二上学期12月质量检测数学试题北京市第五十七中学2021-2022学年高二上学期期末数学试题(已下线)第03讲 空间向量的应用-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第二册)北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题广东省广州市第十六中学2022-2023学年高二上学期期中数学试题广东省广州市第五中学2023-2024学年高二上学期期中数学试题
名校
解题方法
10 . 如图,在直三棱柱
中,
,点
、
分别为
、
的中点,
与底面
所成的角为arctan2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/0c4d2d4e-c2ef-4882-b5b0-fa646c503dc3.png?resizew=155)
(1)求异面直线
与
所成角的大小(结果用反三角函数表示);
(2)求点
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effe94e1c17a1af4575aa461275cdad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42b618e1cd0f3a7c27816d86fbe3907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/0c4d2d4e-c2ef-4882-b5b0-fa646c503dc3.png?resizew=155)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a908f49f9deb228415dcb3d9248aa.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc96c20ebba91031a1c54037fe651c.png)
您最近一年使用:0次
2022-11-06更新
|
265次组卷
|
10卷引用:上海市青浦高级中学2022届高三下学期4月线上质量检测数学试题
上海市青浦高级中学2022届高三下学期4月线上质量检测数学试题上海市青浦高级中学2022届高三4月质检数学试题上海市浦东新区2021届高三三模数学试题上海市大同中学2021届高三三模数学试题上海市向明中学2022届高三上学期9月月考数学试题(已下线)考向23 点、直线、平面之间的位置关系-备战2022年高考数学一轮复习考点微专题(上海专用)沪教版(2020) 选修第一册 新课改一课一练 第4章 阶段复习2(已下线)专题11空间向量与立体几何必考题型分类训练-2上海市复兴高级中学2022届高三上学期10月月考数学试题上海市南洋模范中学2022届高三上学期期中数学试题