1 . 如图,在棱长为1的正四面体
中,
是
的中点,
,
分别在棱
和
上(不含端点),且
平面
.
平面
;
(2)若
为
中点,求平面
截该正四面体所得截面的面积;
(3)当直线
与平面
所成角为
时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a779876cdfb2c489ad0eaed0f73e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(3)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
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名校
解题方法
2 . 如图,在棱长为
的正方体
上,点
为体对角线
靠近
点的三等分点,点
为棱
的中点,点
在平面
上,且在该平面与正方体表面的交线所组成的封闭图形中(含边界),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273990a791754a9bc943874d6ed2ebbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4cba9d2412e4a28f8740bddd5738d4.png)
A.平面![]() ![]() ![]() |
B.点![]() ![]() ![]() |
C.点![]() ![]() ![]() |
D.设平面![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
3 . 一平面截正四棱锥
,与棱
的交点依次为
,已知
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb6099cb3d24e0096b6c2f7aa432abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d659d5601d47fc8e580788f8bfc2cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a2bbe40d86d93964e20a85a84a8bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 下列给出的命题正确的是( )
A.若![]() ![]() |
B.点![]() ![]() ![]() ![]() |
C.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.两个不重合的平面![]() ![]() ![]() |
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解题方法
5 . 在表面积为
的球O的球面上存在A,B,C三点,且
,
,E为线段OC的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a39dce3f1e36dbe01293c309816968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306b21a5d7e68f1992e5797b4368ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397d16b4a33ef2ef92cf7adb5674ec60.png)
A.![]() |
B.异面直线![]() ![]() ![]() |
C.若点O到平面![]() ![]() ![]() ![]() ![]() |
D.若点O到平面![]() ![]() ![]() ![]() |
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6 . 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)
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2024-02-17更新
|
754次组卷
|
5卷引用: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
名校
解题方法
7 . 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
|
267次组卷
|
4卷引用: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
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-(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】
名校
8 . 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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2024-02-03更新
|
1115次组卷
|
5卷引用: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
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
解题方法
9 . 已知向量
,
,则下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ee14381e00c9b46c39d4de41f28d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900b5631dd0aa30d9f8a3a73e87bc04.png)
A.向量![]() ![]() |
B.向量![]() ![]() ![]() |
C.若两个不同的平面![]() ![]() ![]() |
D.若平面![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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10 . 以下四个命题为真命题的是( )
A.已知![]() ![]() ![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.等比数列![]() ![]() ![]() ![]() |
D.若圆![]() ![]() ![]() ![]() ![]() ![]() |
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