名校
1 . 如图,在四棱锥
中,
,
,
,
,
,
,过
的平面
分别交线段
,
于
,
.
![](https://img.xkw.com/dksih/QBM/2023/5/2/3228965501673472/3231243689459712/STEM/e4d93832c6a343cc8f1b803f5e7776f6.png?resizew=285)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969b9971ceae406072933356189a897.png)
(2)若直线
与平面
所成角为
,
,
,求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8eed5763e565f72e7adb33fd366b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e9109f6c3f686ea11ff4ff3b7abecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d917fde8e551e68152595fa0c0cd0aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2023/5/2/3228965501673472/3231243689459712/STEM/e4d93832c6a343cc8f1b803f5e7776f6.png?resizew=285)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969b9971ceae406072933356189a897.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c413808b838e633f62cd922e6405926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf733ac3b5bc538868b9e499021508c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
2023-05-05更新
|
409次组卷
|
2卷引用:福建省厦门第一中学2023届高三下学期4月期中考试数学试题
名校
2 . 如图,在四棱锥
中,
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/9262e594-a819-4f53-9f72-17320ffbc41d.png?resizew=182)
(1)在棱
上是否存在点
,使得
平面
?说明理由;
(2)若
平面
,
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975a48c102d686d23fc2212582af70b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/9262e594-a819-4f53-9f72-17320ffbc41d.png?resizew=182)
(1)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a66d1d242f5317fcc90fee9a8e9fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
您最近一年使用:0次
2023-05-02更新
|
1383次组卷
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4卷引用:福建省厦门双十中学2023届高三热身考试数学试题
3 . 如图,在直三棱柱
中,
,
,
,点M在线段
上,且
,N为线段
上的动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/d1f33241-6f9a-472f-a93d-09978ac0e2a7.png?resizew=114)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209377196940bffa8ffa5f55b9c59fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12405fa4e43fc6ccafa8e5b31bcdb6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/d1f33241-6f9a-472f-a93d-09978ac0e2a7.png?resizew=114)
A.当N为![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.存在点N,使得三棱锥![]() ![]() |
您最近一年使用:0次
2023-04-30更新
|
1175次组卷
|
3卷引用:福建省厦门外国语学校2023届高三适应性考试数学试题
名校
解题方法
4 . 如图,在平行六面体
中,
,
分别是
,
的中点,以
为顶点的三条棱长都是
,
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/5078bccf-e06d-4fb9-82ca-f9028372c7fa.png?resizew=176)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41594dfc1201274ca10aeff335538bdd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/5078bccf-e06d-4fb9-82ca-f9028372c7fa.png?resizew=176)
A.![]() ![]() |
B.![]() |
C.四边形![]() ![]() |
D.平行六面体![]() ![]() |
您最近一年使用:0次
2023-04-19更新
|
1190次组卷
|
6卷引用:福建省厦门市双十中学2022-2023学年高二下学期期中数学试题
名校
5 . 如图,在直三棱柱
中,
,D是棱
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/4fc19a80-bd69-49f7-bf56-58fe950a63a2.png?resizew=153)
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512cc5f78111d4592f6d843db6915f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd25759a3bb1f1283f93e7f2b1c5774.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/4fc19a80-bd69-49f7-bf56-58fe950a63a2.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896d66e2af642634094aec5187f29a21.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e0254c84e44728749b34c08c28ab1e.png)
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2023-04-19更新
|
164次组卷
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18卷引用:福建省厦门集美中学2022届高三12月月考数学试题
福建省厦门集美中学2022届高三12月月考数学试题2015-2016学年河北冀州中学高一下首次月考理科数学卷天津市南开中学2017届高三第五次月考数学(文)试题2020届北京市密云区高三第二学期第二次阶段性测试数学试题吉林省吉化第一高级中学校2020-2021学年高二11月月考数学(理)试题云南省保山市第九中学2019-2020学年高二下学期期中考试数学(理)试题陕西省西安市重点高中2021-2022学年高三上学期第一次考试理科数学试题江苏省扬州市公道中学2020-2021学年高二下学期第二次学情测试数学试题甘肃省天水市第一中学2021-2022学年高三上学期第一次考试 数学(理科)试题北京市第十五中学2022届高三上学期期中考试数学试题云南省弥勒市第一中学2021-2022学年高二上学期第二次月考数学试题黑龙江省双鸭山市第一中学2021-2022学年高二上学期期末数学试题北京市海淀区首都师范大学附属中学2022届高三下学期三模练习数学试题甘肃省武威市凉州区2021-2022学年高二下学期期末考试数学(理)试题陕西省安康市白河高级中学实验班2021-2022学年高二上学期期末理科数学试题(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项(已下线)专题11 空间角的计算(重点突围)(2)(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点1 平面法向量求法及其应用(一)【培优版】
名校
解题方法
6 . 在正方体
中,
为线段
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
A.![]() ![]() |
B.![]() ![]() |
C.三棱锥![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2023-03-14更新
|
868次组卷
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2卷引用:福建省厦门第二中学2022-2023学年高一下学期5月阶段性考试数学试题
名校
解题方法
7 . 已知四面体的四个面均为直角三角形(如图所示),则该四面体中异面直线AB与CD所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/00397c0a-68bf-40c1-8829-63030c0d32a4.png?resizew=294)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/00397c0a-68bf-40c1-8829-63030c0d32a4.png?resizew=294)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-03-07更新
|
312次组卷
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5卷引用:福建省厦门第一中学2022-2023学年高二下学期6月月考数学试题
福建省厦门第一中学2022-2023学年高二下学期6月月考数学试题陕西省安康市2023届高三下学期二模理科数学试题(已下线)湖南省株洲市2023届高三下学期一模数学试题变式题1-5(已下线)专题25 异面直线所成角-2河南省开封市通许县2023届高三三模文科数学试题A卷
解题方法
8 . 如图,在直四棱柱ABCD-A1B1C1D1中,AB⊥AD,CD⊥AD,A1D⊥BD1.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/d2cffa10-bf25-417c-b2c0-5617b187c97c.png?resizew=260)
(1)证明:四边形ADD1A1为正方形;
(2)若直线BD1与平面ABCD所成角的正弦值为
,CD=2AB,求平面ABD1与平面BCD1的夹角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/d2cffa10-bf25-417c-b2c0-5617b187c97c.png?resizew=260)
(1)证明:四边形ADD1A1为正方形;
(2)若直线BD1与平面ABCD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
您最近一年使用:0次
2023-03-07更新
|
1232次组卷
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3卷引用:福建省厦门市2023届高三下学期第二次质量检测数学试题
名校
9 . 已知正四棱锥
的所有棱长均为
,
,
分别是
,
的中点,
为棱
上异于
,
的一动点,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c767ba8ba0ac1fc157fc345cea965.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/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.异面直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.![]() ![]() |
D.存在点![]() ![]() ![]() |
您最近一年使用:0次
2023-02-14更新
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2403次组卷
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8卷引用:福建省厦门第一中学2023届高三二模数学试题
福建省厦门第一中学2023届高三二模数学试题湖南省四大名校名师团队2023届高三普通高校招生统一考试数学模拟冲刺卷(一)浙江省杭州第二中学2023届高三下学期3月月考数学试题山东省淄博实验中学、淄博齐盛高中2022-2023学年高三下学期3月阶段性诊断检测数学试题(已下线)专题8.12 空间直线、平面的垂直(一)(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)广东省佛山市南海区华南师范大学附属中学南海实验高级中学2023届高三保温考数学试题湖南省怀化市长沙市长郡中学等3校2023届高三上学期开学考试数学试题(已下线)专题09 立体几何初步
名校
解题方法
10 . 如图,在四棱锥
中,
底面
,底面
是直角梯形,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633bf2de732ae51fc06ef3d559915da0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/6b42fc9a-243f-4cbf-96ab-e7c4c42dd1af.png?resizew=165)
(1)证明:
平面
;
(2)若
,求三棱锥
的体积.
![](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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633bf2de732ae51fc06ef3d559915da0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/6b42fc9a-243f-4cbf-96ab-e7c4c42dd1af.png?resizew=165)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b459d1f3f6ff1bed5911663604f4e0b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482ee1668a59ca21f3ae8b6bad58eae.png)
您最近一年使用:0次