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:沪教版(2020) 必修第二册 新课改一课一练 第8章 8.4.2向量的应用(2)
名校
2 . 设数阵
,其中
、
、
、
.设
,其中
,
且
.定义变换
为“对于数阵的每一行,若其中有
或
,则将这一行中每个数都乘以
;若其中没有
且没有
,则这一行中所有数均保持不变”(
、
、
、
).
表示“将
经过
变换得到
,再将
经过
变换得到
、
,以此类推,最后将
经过
变换得到
”,记数阵
中四个数的和为
.
(1)若
,写出
经过
变换后得到的数阵
;
(2)若
,
,求
的值;
(3)对任意确定的一个数阵
,证明:
的所有可能取值的和不超过
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118fda38f1089b957ed60695e37a536c.png)
![](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/80dfe04216139283a69617e9dad8048f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1f55a7cb35277e770cf834d0daee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75e807cfe386ca9281b99ddf74ffc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada32feac648a845a4df365354cd196e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c866e176c39fd314d3cd3bbe52ba8ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13457c887234afca68b4ab6be353481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b081228ddb76ebe198cdb4e69f2785d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2321ec2ceeba4ca1168f3c64bcad3da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813ba311354d00f71d2115a560d12b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4891337ce2ce5c1f700b8824a03cd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747f43f06177d471d83cda317c39d105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221f88f10c065cf9c855369540113c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15145fa7ce87d4730373560c26d292bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dbb44d7459e2c69c046775664c21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0dbb44d7459e2c69c046775664c21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8466ad670889f417cd21e72f41628a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85351e9d97942d0291e0c4f784a69ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8d70c89336011fb7ba4006a16f0f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f58b8408ad372250925ef59146017c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b69876a0ef00bf3844058e06443013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8466ad670889f417cd21e72f41628a1.png)
(3)对任意确定的一个数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8466ad670889f417cd21e72f41628a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
您最近一年使用:0次
2020-04-16更新
|
468次组卷
|
5卷引用:北京市第八中学2024届高三上学期期中练习数学试题
名校
3 . 关于
、
的方程组
有无穷多组解,实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.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/e05f5c9e444dfe5ec3c1c06aaec1da5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
您最近一年使用:0次