1 . 在三棱柱
中,平面
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/929825ec-dd81-4486-98b1-2103bd357105.png?resizew=174)
(1)证明:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2623e1c4ecbd65ae5e0285c0453ffd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e793c52fdd16cc602eaf753964ec02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd9abf9ec52d85bfe36188e95e6ad6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/929825ec-dd81-4486-98b1-2103bd357105.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403ec256d712cf32d21ed51d71648c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
您最近一年使用:0次
名校
2 . 如图,在三棱锥
中,
,
,
,
,
,
分别为线段
,
上的点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/7b450a34-8cb3-451c-9f80-d35ae0238ac3.png?resizew=131)
(1)证明:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7c18f9db65fcd840b39d7bbd3028c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28597da489dc639750523c83fbc11c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e99aae9fa3f0cd6405461b8db163e8.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aabee6b0c633ffd42f01af2e1fb8a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75dc7cef548ba1fda2b082733baae52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/7b450a34-8cb3-451c-9f80-d35ae0238ac3.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb0f9de2f087af7ef18ee9184d88b51.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69fbd5a9df4c0210604cf1ae2fa7e0c.png)
您最近一年使用:0次
2019-01-23更新
|
508次组卷
|
5卷引用:娄底市2018-2019学年高二上学期期末考试数学(理)试题
名校
3 . 如图,在梯形
中,
,
,
,现将
沿
翻折成直二面角
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/381bc715-77fe-4609-938a-ada15fa13cc5.png?resizew=468)
(Ⅰ)证明:
;
(Ⅱ)若异面直线
与
所成角的余弦值为
,求二面角
余弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de3595bb7c79503fabd75d99196ccb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbced129627233661d88e9663a9e13c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/381bc715-77fe-4609-938a-ada15fa13cc5.png?resizew=468)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82279b14a119057fdd78b85d63e669.png)
(Ⅱ)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
您最近一年使用:0次
2019-01-22更新
|
3818次组卷
|
4卷引用:江西省赣县第三中学2020-2021学年高二12月月考数学(理)试题
4 . 如图,在长方体
中,
,
,点E是线段AB的中点.
求证:
;
求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95db5d71f0d7cdb83e2b6bb25cea42b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62191bcb4f06ed7667c470207a91cf8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0f3ad5d895dcaad4920847c7d9bc00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/d5dd7750-88bb-4975-bd9b-d855ed0e6416.png?resizew=195)
您最近一年使用:0次
2019-01-21更新
|
410次组卷
|
2卷引用:【校级联考】吉林省“五地六校”合作2018-2019学年高二 第一学期期末考试 文科数学试题
5 . 如图所示,
是正三角形,线段
和
都垂直于平面
,设
,
,且
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/4e302267-a7f7-4554-aa51-99c91cf14570.png?resizew=96)
(1)求证:
平面
;
(2)求证:
;
(3)求平面
与平面
所成的较小二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3b1722b100297f2fa8fad62423149d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede69346d90f2c2c7d738d90c6aa60a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/4e302267-a7f7-4554-aa51-99c91cf14570.png?resizew=96)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f44f2b2f82a9126223138972850aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
6 . 如图,已知矩形ABCD所在平面外一点P,
平面ABCD,E、F分别是AB、PC的中点.
求证:(1)
共面;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edaf1e8554f3be29c6d9b94c2413d04.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b833db5aa6e38de0cdd55bcab1c74c27.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/33bb53cd-a13b-4ecb-8d5e-0ef6880cec47.png?resizew=152)
您最近一年使用:0次
2019-01-16更新
|
2625次组卷
|
12卷引用:江苏省泰州市田家炳中学2017-2018学年度第二学期高二第二次学情调研考试数学(理)
江苏省泰州市田家炳中学2017-2018学年度第二学期高二第二次学情调研考试数学(理)(已下线)专题1.3 空间向量的应用(A卷基础篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教A版,浙江专用)山西省太原市第五十六中学2021-2022学年高二上学期10月月考数学试题(已下线)第1.5讲 用空间向量研究直线和平面的位置关系-2021-2022学年高二数学链接教材精准变式练(人教A版2019选择性必修第一册)内蒙古乌兰察布市2021-2022学年高二上学期期末考试数学(理)试题江苏省宿迁市泗阳县实验高级中学2021-2022学年高二下学期第一次月考数学试题第三章空间向量与立体几何单元检测B卷(综合篇)-2021-2022学年高二上学期北师大版(2019)数学选择性必修第一册(已下线)模块三 专题4 空间点、直线平面与空间向量 A基础卷(人教B)(已下线)第一章 空间向量与立体几何(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)新疆维吾尔自治区喀什地区巴楚县第一中学2023-2024学年高二上学期期末数学试题(已下线)专题8.6 空间向量及其运算和空间位置关系(精练)-2021年新高考数学一轮复习学与练(已下线)第05讲 空间向量及其应用 (高频考点—精讲)-2
解题方法
7 . 如图,在棱长为2的正方体
中,
、
分别为棱
、
的中点,
是线段
上的点,且
,若
、
分别为线段
、
上的动点,则
的最小值为__________ .
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8d4fa054fc8146baf920bb3871d0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f618c20607afa7c345e81d33878148.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/a9022aa1-2e8b-486b-81e6-6c3afd1f1b3a.png?resizew=175)
您最近一年使用:0次
2018-12-29更新
|
1618次组卷
|
3卷引用:山西省运城市景胜中学2020-2021学年高二上学期9月月考数学试题
山西省运城市景胜中学2020-2021学年高二上学期9月月考数学试题【校级联考】湖南省三湘名校2019届高三第二次大联考数学理试题(已下线)第33练 空间角与距离-2021年高考数学(理)一轮复习小题必刷
8 . 如图,四棱锥P﹣ABCD的底面为矩形,侧棱PA⊥底面ABCD,且PA=AD,E,F分别是线段PA,PD的中点,H在线段AB上.
(1)求证:PC⊥AF;
(2)若平面PBC∥平面EFH,求证H是AB的中点;
(3)若AD=4,AB=2,求点D到平面PAC的距离.
(1)求证:PC⊥AF;
(2)若平面PBC∥平面EFH,求证H是AB的中点;
(3)若AD=4,AB=2,求点D到平面PAC的距离.
![](https://img.xkw.com/dksih/QBM/2018/12/13/2095992765210624/2097427692273664/STEM/04bfa9520c1a4a19ada3cee5d8f2745b.png?resizew=152)
您最近一年使用:0次
名校
9 . 如图,在三棱锥
中,
分别为
,
的中点,点
在
上,且
底面
.
(1)求证:
平面
;
(2)若
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8e069903c96854ac0544fe6079f106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6a9cc2bfbe6e294fc68824899dfdf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/6e0d0b92-6b53-47eb-bce7-a59aef9d3401.png?resizew=155)
您最近一年使用:0次
2018-11-18更新
|
2649次组卷
|
4卷引用:海南省海口市第四中学2020-2021学年高二上学期期中考试数学试题