名校
解题方法
1 . 如图所示,多面体是由底面为
的直四棱柱被截面
所截而得到的,该直四棱柱的底面为菱形,其中
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/fa37abea-6c0c-4b50-ba26-933196123560.png?resizew=119)
(1)证明四边形
是平行四边形;并求
的长;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ada1cd3d6b1b2b559468778412ea0e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/fa37abea-6c0c-4b50-ba26-933196123560.png?resizew=119)
(1)证明四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,底面
是边长为2的正方形,侧面
为等边三角形,顶点
在底面上的射影在正方形
外部,设点
,
分别为
,
的中点,连接
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/ffdd15f5-0ccd-4389-a1d5-8442287af7e6.png?resizew=187)
(1)证明:
平面
;
(2)若四棱锥
的体积为
,设点
为棱
上的一个动点(不含端点),求直线
与平面
所成角的正弦值的最大值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/ffdd15f5-0ccd-4389-a1d5-8442287af7e6.png?resizew=187)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbbe7f48676298f2ee0cb1901992eaf.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c9298da3cd8b9db58692e0173f3fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-11-11更新
|
339次组卷
|
3卷引用:福建省泉州市永春第一中学2023-2024学年高二上学期期中数学试题
名校
3 . 在四棱锥
中,
底面
,且
,四边形
是直角梯形,且
,
,
,
,
为
中点,
在线段
上,且
.
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.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/adc90c2d45477e166b02359525f40aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfacd208d769d01f1d4ef20313cd869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
您最近一年使用:0次
2023-10-15更新
|
385次组卷
|
2卷引用:福建省福州市高新区第一中学(闽侯县第三中学)2024届高三上学期12月月考数学试题
4 . 如图,
平面
,
.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07013206f53d36de080c451a7a2a1266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411d1139c919736044af6379743b3d5c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/1de5508f-7c17-43b0-b503-4cd6edebedc8.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
2023-09-26更新
|
562次组卷
|
4卷引用:福建省福州市平潭县新世纪学校2023-2024学年高二上学期12月适应性练习数学试题
福建省福州市平潭县新世纪学校2023-2024学年高二上学期12月适应性练习数学试题天津市双港中学2022-2023学年高二上学期期末数学试题(已下线)模块一 专题2 利用空间向量解决立体几何问题 (讲)2 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)第02讲:空间向量与立体几何交汇(必刷6大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019选择性必修第一册)
名校
5 . 如图所示,等边
所在平面与菱形
所在平面相垂直,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
平面
;
(2)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba4d0b54a0b2104e1c3a2061e4bffc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9087c01257b50f3bb8b6490d8804dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b85d7d422571c4cc3aa5e09505fd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2023-08-16更新
|
528次组卷
|
2卷引用:福建省厦门第一中学2022-2023学年高二下学期期中数学试题
解题方法
6 . 如图,三棱台
中,
,D是AC的中点,E是棱BC上的动点.
平面
,确定
的位置.
(2)已知
平面ABC,且
.设直线
与平面
所成的角为
,试在(1)的条件下,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3258adb95aed2f199d709065c99e6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff368051d372bc2394f3a95a0c4ebca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7291b5dd38e5bd9f962e629f4924217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
您最近一年使用:0次
2023-07-25更新
|
399次组卷
|
5卷引用:福建省福州市八县(市)协作校2022-2023学年高二下学期期末联考数学试题
福建省福州市八县(市)协作校2022-2023学年高二下学期期末联考数学试题(已下线)模块三 专题1 利用空间向量求解探究性问题和最值问题(已下线)专题09 空间向量中动点的设法2种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)通关练04 空间向量与立体几何大题9考点精练(41题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)【人教A版(2019)】专题01立体几何与空间向量(第一部分)-高二下学期名校期末好题汇编
解题方法
7 . 如图,在正三棱柱
中,
,
分别为
,
的中点.
(1)求证:
//平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/19/36876973-2718-4014-a98f-892ea7caee9e.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6357518bce3dd75663f7841de4d26b07.png)
您最近一年使用:0次
名校
8 . 如图,在正三棱柱
中,
,
为
的中点,
、
在
上,
.
(1)试在直线
上确定点
,使得对于
上任一点
,恒有
平面
;(用文字描述点
位置的确定过程,并在图形上体现,但不要求写出证明过程)
(2)已知
在直线
上,满足对于
上任一点
,恒有
平面
,
为(1)中确定的点,试求当
的面积最大时,二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa40b456747f69437444833aab387be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.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/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2564f406fa222935e6d5bb24df0356a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/c34c1d0d-b0de-4ab5-8ff6-a1140bfc6c2c.png?resizew=127)
(1)试在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b17d7abbd564ce785f43a7c8526dc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef68c72248af27e3b83b4ee5fdeb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6b513ee7d966df71cd98b29ca4447e.png)
您最近一年使用:0次
2023-07-09更新
|
864次组卷
|
6卷引用:福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题
福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题福建省永春第一中学2023-2024学年高一上学期8月月考数学试题福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题04 立体几何初步(2)-【常考压轴题】(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】
名校
解题方法
9 . 如图,在直三棱柱
中,
为
的中点,平面
过点
,
,
.
(1)作出
截直三棱柱
的截面,写出作图过程并说明理由;
(2)若
,
,求点
到截面的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/06f0ef54-2417-4148-9ea7-52f9b05e9881.png?resizew=170)
(1)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
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解题方法
10 . 如图,在四棱锥
中,M为PD的中点,E为AM的中点,点F在线段PB上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/fd3f013b-1a62-4901-ae6a-89bd3bf62660.png?resizew=171)
(1)取DM中点G,设平面EFG与直线PC交于点H,再从以下两个条件中选择一个作为已知,求
;
条件①:
;条件②:
∥平面ABCD.
(2)若平面
底面ABCD,
,
,
,
,求平面PAD与平面PBC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/fd3f013b-1a62-4901-ae6a-89bd3bf62660.png?resizew=171)
(1)取DM中点G,设平面EFG与直线PC交于点H,再从以下两个条件中选择一个作为已知,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685856a9b104bd06a26fa1954f2499e8.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afaa76e94414331574f42873e2b12c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795d1f8e68aee16240a4018dcbcb1e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ce06dbe9e1177468781ba4aff85ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64eb3310e5d1aaee7ca7a7889092798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
您最近一年使用:0次
2023-03-07更新
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488次组卷
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2卷引用:福建省华安县第一中学2024届高三上学期开学模拟数学试题