1 . 如图1,在梯形
中,
,
是线段
上的一点,
,
,将
沿
翻折到
的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
为直二面角,
,
分别是
,
的中点,若直线
与平面
所成角为
,
,求平面
与平面
所成锐二面角的余弦值的取值范围;
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
为线段
的中点,
,
分别在线段
,
上(不包含端点),且
为
,
的公垂线,如图3所示,记四面体
的内切球半径为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.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/4eb15c7f8fd604976818ff6de254b6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9d5946fba71d0623ab27f24c6b57fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e184efd65dfaa5d62242c482d2158d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da424b529ab73775b90cd4089d18419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57d8c0d92f5b6bede99e8d9d227e40.png)
您最近一年使用:0次
解题方法
2 . 已知棱长为1的正方体
是空间中一个动平面,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89656654ebe90dfe1f2c243afde60c5d.png)
A.设棱![]() ![]() ![]() ![]() |
B.设棱![]() ![]() ![]() ![]() |
C.正方体的12条棱在平面![]() |
D.四面体![]() ![]() |
您最近一年使用:0次
3 . 如图(1)所示
中,
,
.
分别为
中点.将
沿
向平面
上方翻折至图(2)所示的位置,使得
.连接
得到四棱锥
.记
的中点为
,连接
.
平面
;
(2)点
在线段
上且
,连接
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d390782b8ea7016628ee68403dcbfbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1d18e7acbf1db4243914a885261ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d240ea67c239b0d9213448c11cba18c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aae82d53f2a35d2f95f467bd5b76cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9742fb0549cb89e808d50e81bcef49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef77cfa13de39e9ef424e386f84056e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6592783d1f83c37b051221a7a3a17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f947fd286e0c37fdcc8d1b6ce4295c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-02-17更新
|
749次组卷
|
5卷引用:2024届高三新改革数学模拟预测训练四(九省联考题型)
2024届高三新改革数学模拟预测训练四(九省联考题型)(已下线)模块4 二模重组卷 第2套 复盘卷(已下线)湖北省武汉市(武汉六中)部分重点中学2024届高三第二次联考数学试题变式题17-22山东省济南市2023-2024学年高二上学期1月期末质量检测数学试题山东省临沂市第十九中学2023-2024学年高二下学期第一次质量调研考试数学试题
名校
解题方法
4 . 人教A版选择性必修第一册教材44页“拓广探索”中有这样的表述:在空间直角坐标系中,若平面
经过点
,且以
为法向量,设
是平面
内的任意一点,由
,可得
,此即平面的点法式方程.利用教材给出的材料,解决下面的问题:已知平面
的方程为
,直线
的方向向量为
,则直线
与平面
所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832b5312310a88bef6596496df8daa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38938dd2b6485e6befe9cd0a1b83ec0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff508d982bcd523637373fba322f8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b523a8c1993478f6599680dc3b3dc45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd0c4e77e08b66de9994c8b14efb21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb9a1d7764d138e3110e97551bcd5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-12更新
|
256次组卷
|
4卷引用: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)【基础版】
(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)【基础版】河南省郑州市2023-2024学年高二上学期1月期末考试数学试题江西省宜春市宜丰中学2023-2024学年高二下学期3月月考数学试题河南省周口市西华县第三高级中学2023-2024学年高二下学期第一次月考数学试题-
名校
5 . 在图1所示的平面多边形中,四边形
为菱形,
与
均为等边三角形.分别将
沿着
,
翻折,使得
四点恰好重合于点
,得到四棱锥![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e52045125fa10787dcd577c38147bd.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/3e86ac98-85f0-4774-82e0-0339c4a48245.png?resizew=328)
(1)若
,证明:
;
(2)若二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d668c1a65824451fb5cb2908e4fc229f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b42d15b184904764e9a374554fc589c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06106b41c659977a527753f2736c9f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5262192e49cf903ee094457dbc250f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722932a41451ef41599d297bf10339c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e52045125fa10787dcd577c38147bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e23c8a2244688ed4c848bc4fb4ca576.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/3e86ac98-85f0-4774-82e0-0339c4a48245.png?resizew=328)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036de574712cad14bddadf6653c7e714.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daffe333e60992bb4590370b79b806d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-02-03更新
|
1110次组卷
|
5卷引用:广东省2024届高三数学新改革适应性训练二(九省联考题型)
广东省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)(新高考新结构)2024年高考数学模拟卷(二)(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点8 平面图形的翻折、旋转综合训练湖北省十堰市2023-2024学年高二上学期期末调研考试数学试题重庆市乌江新高考协作体2023-2024学年高二下学期开学学业质量联合调研抽测数学试题
名校
解题方法
6 . 如图,将圆
沿直径
折成直二面角,已知三棱锥
的顶点
在半圆周上,
在另外的半圆周上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7df4e362-6b02-418c-b46e-03f9a8d24516.png?resizew=147)
(1)若
,求证:
;
(2)若
,
,直线
与平面
所成的角为
,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d352cc181bd3e1172014eadc9ab0e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c74fb8e175ebc3bd48a791b7371a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771b610e4ddefa739a985d1e5462ce5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7df4e362-6b02-418c-b46e-03f9a8d24516.png?resizew=147)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faec879692b23ee31c5deb95f2524ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de6dce28eda82f5373eeac1a04ebb40.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4a85e7cdbebd03a5557720988fb604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f457418e6a7e21f0ed0bf490a3709c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
名校
7 . “阳马”是我国古代数学名著《九章算术》中《商功》章节研究的一种几何体,即其底面为矩形,一条侧棱垂直于底面的四棱锥.如图,四棱锥
中,四边形
是边长为3的正方形,
,
,
.
是一个“阳马”;
(2)已知点
在线段
上,且
,若二面角
的余弦值为
,求直线
与底面
所成角的正切值.
![](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/91d5a57d368261e7a0a61d8386459eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8337d3e8670a9ed0165ac853b80af3d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cee96ca90f9f26644860329443ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
(2)已知点
![](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/69e27dea946df6947fb791374c992dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f351b3ffc75878acdbbe4d4926524f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5930602f8d9bb301d34db872d7a3cd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-01-26更新
|
1505次组卷
|
6卷引用:山西省太原市2024届高三上学期期末学业诊断数学试题
解题方法
8 . 已知正方体
的棱长为1,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.从该正方体的所有棱中任选两条,则这两条棱所在的直线异面的概率为![]() |
B.将直线![]() ![]() ![]() ![]() ![]() |
C.将正方体![]() ![]() ![]() |
D.将正方体![]() ![]() |
您最近一年使用:0次
名校
9 . 如图所示,圆台的上、下底面圆半径分别为
和
为圆台的两条不同的母线.
分别为圆台的上、下底面圆的圆心,且
为等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/d1ec33ef-6414-439c-8a01-5fe56fdfd595.png?resizew=153)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
;
(2)截面
与下底面所成的夹角大小为
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7d791489abcbe5a60c359093981fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cef469b1ee29d124cfd6f62423724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/d1ec33ef-6414-439c-8a01-5fe56fdfd595.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d57c8c293377c6dd5d5aadd5e22b33.png)
您最近一年使用:0次
2024-01-24更新
|
1288次组卷
|
3卷引用:湖南省邵阳市2024届高三第一次联考数学试题
名校
解题方法
10 . 类似平面解析几何中的曲线与方程,在空间直角坐标系中,可以定义曲面(含平面)
的方程,若曲面
和三元方程
之间满足:①曲面
上任意一点的坐标均为三元方程
的解;②以三元方程
的任意解
为坐标的点均在曲面
上,则称曲面
的方程为
,方程
的曲面为
.已知曲面
的方程为
.
的方程(无需说明理由),指出
平面截曲面
所得交线是什么曲线,说明理由;
(2)已知直线
过曲面
上一点
,以
为方向量,求证:直线
在曲面
上(即
上任意一点均在曲面
上);
(3)已知曲面
可视为平面
中某双曲线的一支绕
轴旋转一周所得的旋转面;同时,过曲面
上任意一点,有且仅有两条直线,使得它们均在曲面
上.设直线
在曲面
上,且过点
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f353152c7f589c0caf5f964f803ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a056074124fa54255811544a9d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd047376c4cf1b9992cd8e4fe20df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d287ea4a056d41ba4a1962edd7ad0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9adca4ab5571ac6d246ec24732377ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)已知曲面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7232cb20066a3f4b1ebbf3c44e3a51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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