解题方法
1 . 已知
且
,设
是空间中
个不同的点构成的集合,其中任意四点不在同一个平面上,
表示点
,
间的距离,记集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a65680a7f5b5b93239c7dbdc1edd22.png)
(1)若四面体
满足:
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
①求二面角
的余弦值:
②若
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c84afeae87337f9b22fa12902222d1.png)
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ef3399691fa63838aa0474d25b9dc.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ebfda261c4a27e1fa2ee5fc6d4bdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a65680a7f5b5b93239c7dbdc1edd22.png)
(1)若四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c12f98844971f91baaeed4775a72e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
①求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2898853a3396f0878af9eac934416d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10e0b10442a269fe929eb8e592cb1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c84afeae87337f9b22fa12902222d1.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ef3399691fa63838aa0474d25b9dc.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27d71b7260e008ebefdb79da3a2f3e4.png)
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2 . 如图所示的几何体是一个半圆柱和一个三棱锥的组合体.
是半圆柱的母线,
分别是底面直径BC和
的中点,
是半圆
上一动点,
是半圆
上的动点,
是圆柱的母线,延长
至
点使得
为
的中点,连接
,
构成三棱锥
.
;
(2)当三棱锥
的体积最大时,求平面
与平面
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ebf67d880172b27fefacc3c5b808eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d6cde991efd85f03f8801e745127a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683e17492ad37eeab880209057cb0feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5ae8d145c5ce43e4cfc95fe6f563ed.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e367b683581c7cbe018078168f69efc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b36a70bc52a720ba8750aee4924307.png)
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3 . 如图,有一个正方形为底面的正四棱锥
,各条边长都是1;另有一个正三角形为底面的正三棱锥
,各条边长也都是1.
中,求
与平面
所成角的正弦值,并求二面角
的平面角的正弦值;
(2)现把它俩其中的两个三角形表面用胶水黏合起来,如黏合面
和面
.试问:由此而得的组合体有几个面?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fedaa3f2f2dfa9e03f5c9d12400415c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
(2)现把它俩其中的两个三角形表面用胶水黏合起来,如黏合面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1657f0781f2d325a939ebc926e4f4f6.png)
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2卷引用:重庆市巴蜀中学校2024届高三下学期高考适应性月考(九)(4月)数学试题
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4 . 如图,ACDE为菱形,
,
,平面
平面ABC,点F在AB上,且
,M,N分别在直线CD,AB上.
平面ACDE;
(2)把与两条异面直线都垂直且相交的直线叫做这两条异面直线的公垂线,若
,MN为直线CD,AB的公垂线,求
的值;
(3)记直线BE与平面ABC所成角为
,若
,求平面BCD与平面CFD所成角余弦值的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c99e6d75d606b5cae9392ecca969200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f31a3724c639f88486f8356ca65397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
(2)把与两条异面直线都垂直且相交的直线叫做这两条异面直线的公垂线,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3177a657a66974f53b49dc827b78c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e66082fe6f392885b1e57db9ffb5602.png)
(3)记直线BE与平面ABC所成角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e46b60660836022a46da90173c8ef2e.png)
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5 . 2023年12月19日至20日,中央农村工作会议在北京召开,习近平主席对“三农”工作作出指示.某地区为响应习近平主席的号召,积极发展特色农业,建设蔬菜大棚.如图所示的七面体
是一个放置在地面上的蔬菜大棚钢架,四边形ABCD是矩形,
m,
m,
m,且ED,CF都垂直于平面ABCD,
m,
,平面
平面ABCD.
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09030a47bf268b6ea0c341ca76c2358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8fe3b14007e4be4c99c85e5b9610a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d824078abdd94782c09ccc39ddb539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f43ee6bef36a3a67b497cb2e67f4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17980426cd9d489706fdc45b81b9f92.png)
(2)求平面BFHG与平面AGHE所成锐二面角的余弦值.
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4卷引用:重庆市开州中学2024届高三下学期高考模拟考试(二)数学试题
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6 . 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)
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5卷引用: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
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
名校
解题方法
7 . 正方体
中,
,点
在线段
上.
时,求异面直线
与
所成角的取值范围;
(2)已知线段
的中点是
,当
时,求三棱锥
的体积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39ee40b5a17a31195e83ec5f8e0b819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2866bff71c094e32c1320690fff746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459f78e4a3516d8a8535290ede7f386.png)
(2)已知线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef1f7b9adab87736321e30949a4d668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ae9162a1b3fb9c0a1a5a2b014cc45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7432bd55e1f1c618c9908e6377779c9.png)
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2024-01-08更新
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3卷引用:重庆市黔江中学校2023-2024学年高二上学期10月考试数学试题
重庆市黔江中学校2023-2024学年高二上学期10月考试数学试题(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点5 面积、体积的范围与最值问题(三)【基础版】2024年普通高等学校招生全国统一考试数学模拟预测(一)(全国九省联考新题型适用)
名校
解题方法
8 . 如图1,已知
,
,
,
,
,
.
绕
轴旋转半周(等同于四边形
绕
轴旋转一周)所围成的几何体的体积;
(2)将平面
绕
旋转到平面
,使得平面
平面
,求异面直线
与
所成的角;
(3)某“
”可以近似看成,将图1中的线段
、
改成同一圆周上的一段圆弧,如图2,将其绕
轴旋转半周所得的几何体,试求所得几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee80939187a84e1863eeb192a301c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e87b3d349194312a934fced615e563c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3752eaf8b6f65d3faf930dc54bf2ef1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40540618c5b9bb0de570d4c742efe648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65816deab5057903d4b9cb09d6190b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f768ec9a3a36cab9c488149507fd199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)将平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ec6cf562ec0322dd2df37fbf56ef3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af048430d955eb2f6ba0f1cc4bc10243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fe246270d1277f9eb2bf15af22e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)某“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520bbc5e258f1b50b905af41f321ac15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2023-11-16更新
|
534次组卷
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3卷引用:重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷
重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷上海市进才中学2023-2024学年高二上学期期中数学试题(已下线)第二章 立体几何中的计算 专题三 空间体积的计算 微点4 四面体体积公式拓展综合训练【培优版】
名校
9 . 图甲中等腰梯形
的中位线为
,
,
,
,现将梯形沿
折起,使得平面
平面
,如图乙所示.
(1)在图乙中,
,
分别是
,
的中点,证明:
∥平面
;
(2)求图乙中平面
和平面
夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db4bd2cb84e75b6f8de1fa79e87ef01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/76066357-02de-4294-b428-3ec044fa957f.png?resizew=501)
(1)在图乙中,
![](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/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
(2)求图乙中平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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10 . 如图,圆台
的上、下底面圆半径分别为1,2,圆台的高为
,
是下底面圆的一条直径,点
在圆
上,且
,点
在圆
上运动(
与
在
的两侧),
是圆台的母线,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/f355f02f-e5dd-4d70-9e84-8964307ae36b.png?resizew=154)
(1)求
的长;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf271d6475f5305bc922677b4cfe28c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/f355f02f-e5dd-4d70-9e84-8964307ae36b.png?resizew=154)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
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