1 . 如图,在四棱锥
中,
平面
,底面
为直角梯形,
,
,
为
的中点.
(1)证明:
.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af36689a2d2a5f999b3b5859a3c9faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31613f00068be209424c69214a1deb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/7dafc9ee-6a1a-48a3-bd73-5fbaa05cded5.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d23f34a0d1095678f4532f2a7f4c05.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f9bc6bf8ca426813d10b6db2e32d26.png)
您最近一年使用:0次
2023-07-11更新
|
884次组卷
|
5卷引用:陕西省汉中市2022-2023学年高二下学期期末理科数学试题
陕西省汉中市2022-2023学年高二下学期期末理科数学试题云南省楚雄州2022-2023学年高二下学期期末考试数学试题内蒙古名校联盟2022-2023学年高二下学期期末考试理科数学试题(已下线)1.4 空间向量应用(精练)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)第一章 空间向量与立体几何(知识归纳+6类题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
解题方法
2 . 如图,在四棱锥
中,
平面
,底面
为直角梯形,
,
,
为
的中点.
(1)证明:
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83b76a280fc562446ee8ddd2d6bf1d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31613f00068be209424c69214a1deb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/14/673bf6db-8450-4671-9068-ad7098d25a90.png?resizew=155)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d23f34a0d1095678f4532f2a7f4c05.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14eec658f69c267a70c1e8f9b744e282.png)
您最近一年使用:0次
2023-07-11更新
|
260次组卷
|
2卷引用:陕西省汉中市2022-2023学年高二下学期期末文科数学试题
解题方法
3 . 如图,矩形
所在平面与半圆弧
所在平面相交于直线
为半圆弧
上的动点,
平面
.
(1)求证:
平面
;
(2)若
,当
为
的中点时,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53e0cf41726a338dfd99ddff269f19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/13/7921bc6b-9d3e-4229-bf5d-d6ec721dcf4a.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b37fa0ac11bdd407b568bc8c13f310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
4 . 在四棱锥
中,底面
是边长为2的正方形,
,
.
(1)证明:平面
⊥平面
.
(2)若
,求
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/9e74e05a9adf6a1f7a10edd0ac720311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feedf3c1dee6e7befebf368c092ccd0c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/9/ff9f43b4-2dc1-44c3-b4db-2142cd6afc1c.png?resizew=140)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
解题方法
5 . 如图,在四棱锥
中,底面
为矩形,
,
,
为棱
上任意一点(不包括端点),
为棱
上任意一点(不包括端点),且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6281429827d4967da78783e6a8fd4c3f.png)
;
(2)已知
,
,当三棱锥
的体积取得最大值时,平面
与
交于点
,求
的长.
![](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/9d8455347237248c7701100642c5b119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5ea309886e947ea7cb4b81716206fd.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6281429827d4967da78783e6a8fd4c3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0f093f21717e613ed811af47aacd2c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86943f7ede0949e61e78ccdc8e83177f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5b538bcfb898fcc9d3a2dd8a1b080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在三棱锥
中,
,
为
的中点,
平面
,垂足
落在线段
上,已知
,
,
,
.
(1)求异面直线
,
所成角的大小;
(2)在线段
上存在点
且
,探究二面角
的大小并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0819cd060cdfb72896f379db29a4724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72d83915b41102495fcff91dbdbb0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bd1ffa355edcdc023b5a6b47ca7526.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/8/5668b425-8f58-4606-9348-52db789770ee.png?resizew=161)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3432d20e661779ddcefda76afcc2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9a8d2e4172812913af13badafa4dbb.png)
您最近一年使用:0次
名校
7 . 如图所示,平行六面体
中,以顶点
为端点的三条棱长都是1,且它们彼此的夹角都是
,M为
与
的交点.若
,
,
.
(1)用
,
,
表示
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/876c6a34-7430-4d66-afb6-407d8d2bc38e.png?resizew=168)
(1)用
![](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/d7a046d7060dc843c78af806ee24f556.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136cdd691e63a13b934567ddd7642d85.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在直三棱柱
中,P为
的中点,
,
,
.
(1)证明:
平面
.
(2)若四棱锥
的体积为12,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188dfa1c5859c7d1084abe8adc559df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d915b61de008ad2bf7818fc5eb3cfd15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d39d040c418bb3d2e002020dd3311c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/8f11b86c-7323-4204-8636-7387a5f75436.png?resizew=122)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f61d8d0aaefc3ac491ad3659a2ba2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2059a230ca1793fd4554b8d43e968f43.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b19ac275e614cda283f67a5c6cee2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
您最近一年使用:0次
2023-07-06更新
|
213次组卷
|
2卷引用:陕西省商洛市2022-2023学年高二下学期期末文科数学试题
9 . 如图,
中,
,四边形
是边长为
的正方形,
平面
,若
、
分别是
、
的中点.
(1)求证:
平面
;
(2)求证:
面
;
(3)求
和面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6321a96e7f0768394f6932a121adc84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/8/8fe97e3c-8bbe-4fbd-9c90-985ec00164ef.png?resizew=127)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c27a8fd3bf5b89a16dbbe1a8230653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,已知菱形
和矩形
所在的平面互相垂直,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
.
(1)求直线
与平面
的夹角;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bebae04c72b934bfbbf0b4d01f164f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/6f173dda-36b4-4a96-a0e1-974465d00002.png?resizew=169)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128c69eb81dae89c6989d06d20925ad2.png)
您最近一年使用:0次
2023-07-04更新
|
2112次组卷
|
21卷引用:陕西省宝鸡市渭滨区2018-2019学年高二上学期期末数学(理)试题
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