1 . 如图一,在平面直角坐标系
中,
为坐标原点,
,
,请根据以下信息,处理问题(1)和(2).信息一:
为坐标原点,
,若将
顺时针旋转
得到向量
,则
,且
;信息二:
与
的夹角记为
,
与
的夹角记为
,则
;信息三:
;信息四:
,叫二阶行列式.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
,(外层“
”表示取绝对值);
(2)如图二,已知三点
,
,
,试用(1)中的结论求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effc7768e61293768fcaf8c8979ff109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36be470b9902a88939057d2f55280e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad852a240fd16f5430472a3ff8c4063c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98afd2734ffaecbcb49e17416de7f062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81a1c2ae937c87ee40f6b5d3e06bee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e7b25d10dbe02750492faf9d0cd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd483afbcdcd303e0c66ab48838bedfc.png)
(2)如图二,已知三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773c2dd14d50e7f0d3326af4833d899a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5249114b149be585bc9b0fa1ae77e4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
您最近一年使用:0次
2020-08-03更新
|
220次组卷
|
2卷引用:贵州省贵阳市2019-2020学年高一下学期期末考试数学试题
2 . 系数行列式
是二元一次方程组
有唯一解的( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d40dc2a11aa3396544980a65d1e5449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65bd6cdc598a67059dc4293a1694dc0.png)
A.充分非必要条件 | B.必要非充分条件 |
C.充要条件 | D.既非充分又非必要条件 |
您最近一年使用:0次
3 . 满足方程
的一个解是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0912431f93d571f687831600f4d8ce30.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知矩阵
.
(1)计算
;
(2)通过第(1)小题的计算猜想
的结论
;
(3)用数学归纳法证明你的结论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6e1b0671e5a92cfb1a5ad939962ad2.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6a5e6b0e2ecf059e35675f5276ea96.png)
(2)通过第(1)小题的计算猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab9d5b4d50800fadbec4246b28fd051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fc82353331abee0828dee9b38c08f2.png)
(3)用数学归纳法证明你的结论
您最近一年使用:0次
5 . 求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3a8ada49fafd592b8f923ce9e7abe6.png)
您最近一年使用:0次
6 . 函数
的最大值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4071522bcae6910b92f1a49bca6fe651.png)
您最近一年使用:0次
7 . 不等式
的解集是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1164ef9254223cefae576efa1e471c6.png)
您最近一年使用:0次
8 . 不等式
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c8bdbe3e1329acb8782e77d5d7a099.png)
您最近一年使用:0次
9 . 求和:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518b6a8a080ded0813c4d444ada42ea7.png)
您最近一年使用:0次
10 . 已知
.求证:
三点共线的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39d023fc87895b0f26477e890074e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7358ff8d99126de46113bb1c1c50f726.png)
您最近一年使用:0次