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1 . 等腰梯形
中,
,
,
.若点
、
均在
上,且
.如图(一)所示,沿
将
折起,沿
将
折起,使
、
两点重合为
.
(1)若
,如图(二)所示,求证:平面
平面
;
(2)若
,
为
中点,当
与
重合于
时,如图(三)所示,求
与平面
所成角的余弦值;
(3)请设计一个翻折方案使四棱锥
的外接球半径为
,证明你的结论,并求此方案下的
的长度及
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b040eb31b0b7073ad3ffa8bd7968d187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.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/04f8eebda19eded2b059774a8c2666c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/ba897f14-f9d7-44dc-b819-8c1cfd0adc02.png?resizew=459)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27aa17bad024a9361bd0a679e10f70ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bec37dca00db5f4512ce70f16ceb20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3747e528a1e8d45668ccf835c0175a73.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(3)请设计一个翻折方案使四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff027309f3108559e6b3915158a3867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b0b11a80e8b107e55534d7fda9f2b.png)
您最近一年使用:0次
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解题方法
2 . 如图一:球面上的任意两个与球心不在同一条直线上的点和球心确定一个平面,该平面与球相交的图形称为球的大圆,任意两点都可以用大圆上的劣弧进行连接.过球面一点的两个大圆弧,分别在弧所在的两个半圆内作公共直径的垂线,两条垂线的夹角称为这两个弧的夹角.如图二:现给出球面上三个点,其任意两个不与球心共线,将它们两两用大圆上的劣弧连起来的封闭图形称为球面三角形.两点间的弧长定义为球面三角形的边长,两个弧的夹角定义为球面三角形的角.现设图二球面三角形
的三边长为
,
,
,三个角大小为
,
,
,球的半径为
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf538440bd45e5881f2b22994560ba7a.png)
(2)①求球面三角形
的面积
(用
,
,
,
表示).
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf538440bd45e5881f2b22994560ba7a.png)
(2)①求球面三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f314e3f1d6311f0476623d4e55484a3e.png)
您最近一年使用:0次
2023-04-21更新
|
384次组卷
|
4卷引用:浙江省A9协作体2022-2023学年高一下学期期中联考数学试题
浙江省A9协作体2022-2023学年高一下学期期中联考数学试题(已下线)13.3 空间图形的表面积和体积(分层练习)江苏省徐州市第一中学2022-2023学年高一下学期期中数学试题(已下线)11.1.5 旋转体-【帮课堂】(人教B版2019必修第四册)
名校
3 . 给定不共面的4点,作过其中3个点的平面,所有4个这样的平面围成的几何体称为四面体(如图所示),预先给定的4个点称为四面体的顶点,2个顶点的连线称为四面体的棱,3个顶点所确定的三角形称为四面体的面.求证:四面体中任何一对不共顶点的棱所在的直线一定是异面直线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/7591e2f1-42ef-474b-ae38-6e946dfe7429.png?resizew=151)
(1)请你用异面直线判定定理证明该结论;
(2)请你用反证法证明该结论.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/7591e2f1-42ef-474b-ae38-6e946dfe7429.png?resizew=151)
(1)请你用异面直线判定定理证明该结论;
(2)请你用反证法证明该结论.
您最近一年使用:0次
解题方法
4 . 如图,在直角梯形
中,
,
,
,并将直角梯形
绕AB边旋转至ABEF.
平面ADF;
(2)求证:直线
平面ADF;
(3)当平面
平面ABEF时,再从条件①、条件②、条件③这三个条件中选择一个作为已知,使平面ADE与平面BCE垂直.并证明你的结论.
条件①:
;
条件②:
;
条件③:
.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6045266f6db39e41b7abde762d9e9a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
(3)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6166b9a5437671bcba31e17c375eb39.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c182a9d9fd0a7023b710cd671d9468e7.png)
您最近一年使用:0次
2022-07-08更新
|
1268次组卷
|
11卷引用:北京市丰台区2021-2022学年高一下学期期末练习数学试题
北京市丰台区2021-2022学年高一下学期期末练习数学试题(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)(已下线)模块三 专题9(劣构题)拔高能力练(北师大版)(已下线)模块三 专题9(劣构题)基础夯实练(人教B)(已下线)模块三 专题9(劣构题)拔高能力练人教A版)(已下线)模块三 专题10(劣构题)拔高能力练(苏教版)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)(已下线)7.2 空间几何中的垂直(精练)(已下线)7.1 空间几何中的平行与垂直(精讲)(已下线)高考新题型-立体几何初步(已下线)2023年高考全国乙卷数学(理)真题变式题16-20
解题方法
5 . 用光线照射物体,在某个平面上得到的影子叫做物体的投影,照射光线叫做投影线,投影所在的平面叫做投影面.由平行光线形成的投影叫做平行投影,由点光源发出的光线形成的投影叫做中心投影.投影线垂直于投影面产生的平行投影叫做正投影,投影线不垂直于投影而产生的平行投影叫做斜投影.物体投影的形状、大小与它相对于投影面的位置和角度有关.如图所示,已知平行四边形
在平面
内的平行投影是四边形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
(1)若平行四边形
平行于投影面(如图
),求证:四边形
是平行四边形;
(2)在图
中作出平面
与平面
的交线(保留作图痕迹,不需要写出过程);
(3)如图
,已知四边形
和平行四边形
的面积分别为
,平面
与平面
的交线是直线
,且这个平行投影是正投影.设二面角
的平面角为
(
为锐角),猜想并写出角
的余弦值(用
表示),再给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/71cf6fa5-9cb4-4d8d-a907-fa7ccdcd6d3d.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/9fc4f21f-3f78-4976-887c-0642c3365737.png?resizew=314)
图
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/462c058d-eb41-4d4a-ac0e-89fb806fef7a.png?resizew=314)
图
(1)若平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
(2)在图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7021666155884a8aa345ed8eec3d2a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
您最近一年使用:0次
20-21高一·全国·课后作业
解题方法
6 . 求证:如果两个平行平面同时与第三个平面相交,那么它们的交线平行(根据如图写出已知、求证并加以证明).
![](https://img.xkw.com/dksih/QBM/2021/4/17/2701599047794688/2703433862283264/STEM/29ecd1acba9745c4b826f63b88862ee6.png?resizew=175)
您最近一年使用:0次
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解题方法
7 . 如图(1),正三棱柱
,将其上底面ABC绕
的中心逆时针旋转
,
,分别连接
得到如图(2)的八面体
,依次连接该八面体侧棱
的中点分别为M,N,P,Q,R,S,
(ⅰ)求证:
共面;
(ⅱ)求多边形
的面积;
(2)求该八面体体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3a008a5ce2f3e0d93bf1b31f1e941d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b73c7e51c2fbe79faa78e5287d2ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ae231960760617a585b8478185d8ac.png)
(ⅱ)求多边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3662c929bd88085eb96dd4797482de.png)
(2)求该八面体体积的最大值.
您最近一年使用:0次
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解题方法
8 . 在通用技术课上,老师给同学们提供了一个如图所示的木质四棱锥模型
,
为正三角形,
,
,
为线段
的中点.
平面
;
(2)过点
的平面
交
于点
,沿平面
将木质四棱锥模型切割成两部分,在实施过程中为了方便切割,请你完成以下两件事情:
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
点的位置,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d94061dfdcef084c7594522ae9e512a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8136c029f4b31e25c56c70a1432cbe1a.png)
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9 . “风筝”是中国传统文化中不可或缺的一部分,距今已有2000多年的历史.相传在东周春秋时期,墨翟以木头制成木鸟,是人类最早的风筝起源.后来鲁班用竹子,改进墨翟的风筝材质,直至东汉期间,蔡伦改进造纸术后,坊间才开始以纸做风筝,称为“纸鸢”.到南北朝时,风筝开始成为传递信息的工具;从隋唐开始,由于造纸业的发达,民间开始用纸来裱糊风筝;到了宋代的时候,放风筝成为人们喜爱的户外活动.风筝主要由骨架、风筝面、尾翼、提线、放飞线五部分组成.如图(1)就是一个由菱形的风筝面ABCD和两个直角三角形尾翼
和
所组成的风筝.其中
,
,
,
,
.现将此风筝的两个尾翼分别沿
折起,使得点P与点Q重合于点S,并连结
,得到如图(2)所示的四棱锥
.
平面
;
(2)若E为棱
上一点,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968088978992ba767468dec2dc436350.png)
①若
求直线
与平面
所成角的正切值;
②是否存在点E使得直线
与直线
所成角为
,若存在请求出
的值,若不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41984f53bb280ba8b5ac00a52ce2825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d899b31ac8800258c52e86a70e7ab9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a0f2f623bbe6beb1fdbc767bc1ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a887678ca42faa3d289e2b6460790b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
(2)若E为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968088978992ba767468dec2dc436350.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
②是否存在点E使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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10 . 三阶行列式是解决复杂代数运算的算法,其运算法则如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
若
,则称
为空间向量
与
的叉乘,其中
,
,
为单位正交基底. 以
为坐标原点、分别以
,
,
的方向为
轴、
轴、
轴的正方向建立空间直角坐标系,已知
,
是空间直角坐标系中异于
的不同两点
(1)①若
,
,求
;
②证明
.
(2)记
的面积为
,证明:
.
(3)证明:
的几何意义表示以
为底面、
为高的三棱锥体积的
倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c685c6a79c8293c8b5083c3a8dc4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e91aaddb8691f8afa477a96bf630631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba64ae92194bc4f0f6e49725471542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8643f24c3af715421ec0ccd3224ed453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d541143135cb9b8166bc631a85ac6a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a471332d4f3731d90f62fdf819f39824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73db31aecdde14e0002f082d9091df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2980a18e4d0a2a795b7983a1a1866db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1821c677712026f8de34fe924b1f52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.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/1dde8112e8eb968fd042418dd632759e.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41ef077626c88964805a45849471a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb22d1c614d99e2639864e43f4b6277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00db2bada2cfc90c5213aca8af17df4c.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb8623a42db5ceb745a16d72739f513.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0505ce82dd5726c22fcaac54d01d630b.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8191a760981f2d67648905665c8b167a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad58b362528b814739ceb7fe5febfc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
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2024-03-07更新
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888次组卷
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8卷引用:专题08 期末必刷解答题专题训练的7种常考题型归类-期末真题分类汇编(北师大版2019必修第二册)
(已下线)专题08 期末必刷解答题专题训练的7种常考题型归类-期末真题分类汇编(北师大版2019必修第二册)河南省部分重点高中2024届高三普通高等学校招生全国统一考试(期末联考)数学试卷江苏省扬州市仪征中学2024届高三下学期期初调研测试数学试题 河南省部分重点高中(青桐鸣)2023-2024学年高三上学期期末大联考数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)江苏省江都中学2023-2024学年高二下学期3月联考数学试卷江苏省盱眙中学2023-2024学年高二下学期第一次学情调研数学试题(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2 平面法向量求法及其应用(二)【培优版】