1 . 如图,三棱柱
所有的棱长均为1,且四边形
为正方形,又
.
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646607720415232/2646698645954560/STEM/dc550430-4f68-4e48-a5ff-84cb4cf9e4df.png)
(Ⅰ)求证:
;
(Ⅱ)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b387bd1fd555508a3c81162ff36a50f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646607720415232/2646698645954560/STEM/dc550430-4f68-4e48-a5ff-84cb4cf9e4df.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f389796c8fa08d8f91e9cbb1a08e438.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
2021-01-29更新
|
829次组卷
|
5卷引用:8.5 空间直线、平面的垂直--2020--2021高中数学新教材配套提升训练(人教A版必修第二册)
(已下线)8.5 空间直线、平面的垂直--2020--2021高中数学新教材配套提升训练(人教A版必修第二册)(已下线)8.6空间直线、平面的垂直(2)(精炼)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)浙江省湖州市2020-2021学年高三上学期期末数学试题湖北省2020-2021学年高二下学期3月联考数学试题浙江省杭州市桐庐分水高级中学2021届高三下学期回头考数学试题
解题方法
2 . 如图所示,
为
的直径,C为
上一点,
平面
,
于E,
于F.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.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/53c51c25b65a37b676ae3c3b71c29f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbee06d305abf6692125513dc3757f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
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解题方法
3 . 已知菱形
的边长为2,
,对角线
、
交于点O,平面外一点P在平面
内的射影为O,
与平面
所成角为30°.
;
(2)点N在线段
上,且
,求三棱锥
的体积.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)点N在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238b75cabddded6f9c1e2626cf67c0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7856360cd4fd774543dff3d7ca03ba85.png)
您最近一年使用:0次
名校
4 . 已知,在四棱锥
中,
底面
,底面
为正方形,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/75b75f3e-f07f-4cc5-8478-b314746c0647.png?resizew=168)
(1)求证:
;
(2)在棱
上是否存在点
,使
?若存在,求BF的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.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/8ee4b29c10915812f832ee29727e74f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/75b75f3e-f07f-4cc5-8478-b314746c0647.png?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3658c9637da0a83d05cccf33bec7e16.png)
(2)在棱
![](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/187ed13a7bd532bd39af5e5ad7493a2c.png)
您最近一年使用:0次
20-21高二上·江西南昌·阶段练习
名校
解题方法
5 . 如图,在四棱锥
中,
平面
,底面
为正方形,F为对角线AC与BD的交点,E为棱PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/d47646ff-38dc-4dbf-ab5d-a15d2e685f8a.png?resizew=162)
(1)证明:
平面PBC;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/d47646ff-38dc-4dbf-ab5d-a15d2e685f8a.png?resizew=162)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
您最近一年使用:0次
2020-11-01更新
|
971次组卷
|
5卷引用:北京市密云区2019-2020学年高一下学期数学期末试题
北京市密云区2019-2020学年高一下学期数学期末试题(已下线)【南昌新东方】 江西省南昌三中2020-2021学年高二上学期10月第一次月考数学(理)试题江西省宜春市上高二中 2020-2021学年高二(上)第三次月考数学(理科)试题江西省上高二中2020-2021学年高二上学期第三次月考数学(理)试题广西贵港市立德高级中学2020-2021学年高二3月月考数学(理)试题
名校
6 . 在四棱锥
中,底面
为正方形,
底面
,
,
为线段
的中点,连接
.
;
(2)连接
,求
与底面
所成角的正切值;
(3)求二面角
的平面角的正切值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de7cb1d10dd759c0ebd487e4ca34ac8.png)
您最近一年使用:0次
2020-09-04更新
|
506次组卷
|
3卷引用:湖北省仙桃市、天门市、潜江市2019-2020学年高一下学期期末数学试题
湖北省仙桃市、天门市、潜江市2019-2020学年高一下学期期末数学试题湖北省武汉西藏中学2022-2023学年高一下学期6月期末数学试题(已下线)专题06 空间直线﹑平面的垂直(一-《知识解读·题型专练》(人教A版2019必修第二册)
19-20高一·全国·课后作业
解题方法
7 . 如图,正方体
中,
与异面直线
、
都垂直相交.
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09475a5c0b23d70f3cd1a31bdecd1d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e89457e4eafe86d2c6f404f967c753.png)
您最近一年使用:0次
2020-08-27更新
|
280次组卷
|
7卷引用:【新教材精创】11.4.1 直线与平面垂直(第2课时)导学案(1)
(已下线)【新教材精创】11.4.1 直线与平面垂直(第2课时)导学案(1)(已下线)8.6.2 直线与平面垂直(精练)(已下线)第13讲 8.6.2直线与平面垂直的性质定理 (第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)专题06 空间直线﹑平面的垂直(一-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)11.4.1直线与平面垂直-同步精品课堂(人教B版2019必修第四册)(已下线)10.3 直线与平面间的位置关系(第2课时)(七大题型)(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)第10章+空间直线与平面(知识清单+典型例题)
19-20高一·全国·课后作业
解题方法
8 . 如图所示,在长方体
中,
平面
,
平面
,且
平面
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c2f227b3ec9a65debb32a0395ffd62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001e90e232a254b9a57dc3339ea265dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303318d7a0b71711f5a72e38ceadf8eb.png)
您最近一年使用:0次
19-20高一·全国·课后作业
解题方法
9 . 四棱锥
如图所示,其中四边形
是直角梯形,
,
,
平面
,
,
与
交于点
,点
在线段
上.若直线
平面
,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.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/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16c60a6ee742a7450aba9cc8415109d.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a829577bb0863d3f39db38ca4c179a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b98851cd97e52ae204272ab60a0a4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/7c880844-5c95-437d-87d4-4bb2c1e9f709.png?resizew=192)
您最近一年使用:0次
名校
解题方法
10 . 如图,在四棱锥P-ABCD中,∠ADB=90°,CB=CD,点E为棱PB的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701089425809408/2701252541497344/STEM/199bd7c60d9944dba3434227686ac2ef.png?resizew=194)
(1)若PB=PD,求证:PC⊥BD;
(2)求证:CE∥平面PAD.
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701089425809408/2701252541497344/STEM/199bd7c60d9944dba3434227686ac2ef.png?resizew=194)
(1)若PB=PD,求证:PC⊥BD;
(2)求证:CE∥平面PAD.
您最近一年使用:0次
2021-04-16更新
|
1558次组卷
|
6卷引用:福建省厦门双十中学2020-2021学年高一下学期期中考试数学试题
福建省厦门双十中学2020-2021学年高一下学期期中考试数学试题(已下线)8.6.1 空间直线、平面的垂直(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)【全国市级联考】江苏省苏锡常镇四市2017-2018学年度高三教学情况调研(二)数学试题【市级联考】江苏省无锡市2019届高三第一学期期末复习数学试题江西省南昌市洪都中学2019-2020学年高二上学期第三次联考理数试题(已下线)解密06 空间点、线、面的位置关系(讲义)-【高频考点解密】2021年新高考数学二轮复习讲义+分层训练