名校
解题方法
1 . 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
|
888次组卷
|
8卷引用: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)(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)
解题方法
2 . 已知函数
.
(1)当
时,求
的值域;
(2)已知
的内角
的对边分别为
,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa80dda69632b3d09cef3c20928a1bc.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b3fb2da3909e643ef238b8d0ac559e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ca18ebee338ac3ca476a10fd88fbd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b3fb2da3909e643ef238b8d0ac559e6.png)
您最近一年使用:0次
3 . 已知矩阵
,
,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ad0004771df5fef239fdb4e219229d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27e8981113be6f5d7a9523ca222bfcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d7366be948699262e4764bbc66dd46.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)求不等式
的解集;
(2)若不等式
在
上恒有解,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a00af37a95128db5d3745a7a327063.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2942e2647554b44127bfce7b22f36a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af98533fbc91ae52c1eeaf0592a86f8.png)
您最近一年使用:0次
2020-08-16更新
|
227次组卷
|
3卷引用:上海市复旦大学附属中学2020-2021学年高二上学期10月月考数学试题
上海市复旦大学附属中学2020-2021学年高二上学期10月月考数学试题上海市行知中学2019-2020学年高一下学期期末数学试题(已下线)大题易丢分必做30题(提升版)-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)
5 . 已知矩阵
满足
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35af899c7ff0d851f6178b4e386595f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b909b41750d5454426fa8c4981a39196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
您最近一年使用:0次
6 . 已知矩阵
,列向量
,
,且
.
(1)求矩阵
的逆矩阵
;
(2)求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1543491ed4c55728e1bc2af73a6ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad77f09909a01ee37d23d4f4dc1bcad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3653fd7a940bc691e60151a6c98722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6d157735b1e5b220fc474ed14a664.png)
(1)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
7 . 设矩阵
,
,若
,求矩阵M的逆矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7998cbff6c266ccf387ebf2d170be4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3976b36f49113841933c96ab5a50fad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ae9b71c32d3684fae2e3d3a0fbd664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
您最近一年使用:0次
8 . 已知矩阵
的一个特征值λ=2,其对应的一个特征向量是
.求矩阵M的另一个特征值以及它的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04753e2b6e63d06984e73e58b8a385a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58be54e080d70b16ba8e31248e742220.png)
您最近一年使用:0次
2020-03-05更新
|
126次组卷
|
2卷引用:2020届江苏省南京十三中、中华中学高三下学期联合调研数学试题
9 . 已知矩阵
,其中
、
,点
在矩阵的变换下得到的点
.
(1)求实数
、
的值;
(2)求矩阵
的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58a98d19c07ee41d4814d2b57f58e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ad0f94243a1600321c4b2b27c307de.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2019-12-27更新
|
85次组卷
|
2卷引用:2020届江苏省南通市四校联盟高三数学模拟试题