1 . 对于任意给定的四个实数
,
,
,
,我们定义方阵
,方阵
对应的行列式记为
,且
,方阵
与任意方阵
的乘法运算定义如下:
,其中方阵
,且
.设
,
,
.
(1)证明:
.
(2)若方阵
,
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e76d1d8e50dda4d50229a8a20c57e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ec97af19b15cd584710a3faf30c716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f44b167b4e75af29a18637f71f3ebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39fcc210ec89dbc7d684a70a34542c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ebf9f595cdb9dab841dec703b512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4ed514630bd37fab9765b3fb5f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709d09c76c222f156df31a1bba5f2ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4a35eca00ea2f4580d62515d54d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95035eeae686e910be45f08093e406c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e7d309cb178b71c6e56f5b7f610413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b4ece615b08a89a7f69d436f448b0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb109c49695bce8c5b5cf4fad95772.png)
(2)若方阵
![](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/2221c60bc15c59fa1b3ac74a23b57cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa9bfe3bf3e3b7265da3c49d31f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35536fb98d8b24cead230c8df95fd9d3.png)
您最近一年使用:0次
2024-06-13更新
|
154次组卷
|
3卷引用:2024届河北省保定市九县一中三模联考数学试题
名校
解题方法
2 . 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)
您最近一年使用:0次
2024-03-07更新
|
891次组卷
|
8卷引用: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
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】(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)
3 . 已知椭圆
,直线
过右焦点
与椭圆交于
、
两点,
的三个顶点均在椭圆上,且
为坐标原点.
(1)小明在计算
的面积的最大值的时候用了如下方法,其中有两处出错,请指出其中的一处错误之处,并说明原因;解答:设
,
,则
,所以
的面积的最大值为
.
(2)请给出题目(1)中问题的正确解答;
(3)小明虽然做错了,但这种方法在计算某些题目时会比常规方法便捷些,如求证下面问题,求证:当
的重心为原点
时,
的面积是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)小明在计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7058164cb469d8769a0d69d9f1f75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e87eaf671d97e2c87b470990d2490e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d15ddd005b859f85ae3f16edc2d8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(2)请给出题目(1)中问题的正确解答;
(3)小明虽然做错了,但这种方法在计算某些题目时会比常规方法便捷些,如求证下面问题,求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
您最近一年使用:0次
解题方法
4 . 设平面直角坐标系中的动点
到两定点
、
的距离之和为
,记动点
的轨迹为
.
(1)求
的方程;
(2)过
上的点
作圆
的两条切线,切点为
、
,直线
与
、
轴的交点依次为异于坐标原点
的点
、
,试求
的面积的最小值;
(3)过点
且不垂直于坐标轴的直线
交
于不同的两点
、
,线段
的垂直平分线与
轴交于点
,线段
的中点为
,是否存在
,使得
成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc8350b12974ffc8d06fce36d158f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c81d490c018a166d9970b1b5ea0a63.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f52b152eaf63415b10ed786a58a2747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e20268889bf68598593b75d240e4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e027f5865860c6c6e224f47b4140e1d9.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e475051ef1977472b714c10a994cd680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7d87f0533f5e9212f98dce720a0ebc.png)
您最近一年使用:0次
5 . 由
个互不相等的正数组成的矩阵
中,每行中的三个数成等差数列,且
、
、
成等比数列,下列判断正确的有
①第
列中的
必成等比数列;②第
列中的
不一定成等比数列;③
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d537d58c1657629b053368830666779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb9d1aa1cc02e6fe13141ecf5f2549b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab5310774cd482fffd19586983b44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f39dd97b907f10708e0dc75076f8a.png)
①第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e656f8468f99e0f5e60fd190893299af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a6f6b78f8f195a961634727d8c934f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a483f03e2a7fd4769bc50f184692d3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次