名校
解题方法
1 . 如图,在长方体
中,点E、F分别在
,
上,且
,
.
平面
;
(2)当
,
,
时,求平面
与平面
的夹角的余弦值.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4305d8d52fe2cc79c78129652e64bb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fccb37728702288d4be7148301ab685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6bf42c7db96104456424e4d1be6c48.png)
您最近一年使用:0次
2022-01-21更新
|
453次组卷
|
10卷引用:河南省许昌市2020-2021学年高二上学期期末数学(理)试题
名校
2 . 如图,四棱锥P-ABCD中,底面ABCD为正方形,△PAB为等边三角形,平面PAB⊥底面ABCD,E为AD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/7d280fd2-8553-4456-8903-7c3564b13a64.png?resizew=215)
(1)求证:CE⊥PD;
(2)在线段BD(不包括端点)上是否存在点F,使直线AP与平面PEF所成角的正弦值为
,若存在,确定点F的位置;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/7d280fd2-8553-4456-8903-7c3564b13a64.png?resizew=215)
(1)求证:CE⊥PD;
(2)在线段BD(不包括端点)上是否存在点F,使直线AP与平面PEF所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
您最近一年使用:0次
2021-12-01更新
|
1334次组卷
|
11卷引用:河南省许昌市2020-2021学年高二下学期期末数学(理)试题
河南省许昌市2020-2021学年高二下学期期末数学(理)试题河北省石家庄市2021届高三二模数学试题(已下线)专题06 空间向量与立体几何(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)专题04 空间向量与立体几何的压轴题(二)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)福建省福州高级中学2021-2022学年高二上学期期中考试数学试题福建省福州市连江尚德中学等六校2021-2022学年高二上学期期中考数学试题广东省华中师范大学海丰附属学2021-2022学年高二上学期期中数学试题(已下线)7.6 空间向量求空间距离(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)四川省安岳县周礼中学2022-2023学年高二上学期期末测数学理科试题广东省东莞实验中学2022-2023学年高二上学期期中数学试题福建省南平市南平一中2023-2024学年高二上学期第一次月考数学试题
解题方法
3 . 如图,在四棱台
中,底面四边形
为菱形,
,
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/b356c562-c7f0-47f5-a6c2-3f8803183605.png?resizew=176)
(1)若点
是
的中点,求证:
;
(2)设棱
上靠近
的四等分点为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90301105ac42d03dd051753436169f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/b356c562-c7f0-47f5-a6c2-3f8803183605.png?resizew=176)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e87a48373fec0d84a3cda27fbd33e7e.png)
(2)设棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/54ad0edb590fa1cc97383714f87cbda6.png)
您最近一年使用:0次
4 . 如图所示,空间多面体
中,
为正方形,
为梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c399688f82087a8ed12cd4ac5c07dbb.png)
,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634620439855104/2637845906382848/STEM/6499fb86-05da-489d-958e-83684e2577b6.png?resizew=186)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c399688f82087a8ed12cd4ac5c07dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bc86e894faa9cd073fe9b455b3ff8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634620439855104/2637845906382848/STEM/6499fb86-05da-489d-958e-83684e2577b6.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147310251a463539f66374c1f452fb67.png)
您最近一年使用:0次
名校
5 . 图1是由平行四边形ABCD和
组成的一个平面图形.其中
,
,
,将
沿AB折起到
的位置,使得
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b3831aa7-f701-40d7-99bf-1bd426d46105.png?resizew=403)
(1)证明:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a3b94566843e92ce775ff6bdf386fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a61fdf950d8e03d11ebe815685e499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5753a5af8f527fdb0f6a53f6ace72ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b3831aa7-f701-40d7-99bf-1bd426d46105.png?resizew=403)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b07e317ffe7859e81b42ef4970e344a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
您最近一年使用:0次
2020-08-07更新
|
306次组卷
|
2卷引用:河南省许昌实验中学2020-2021学年高二下学期期末数学(理科)试题