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
|
218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 . 若
表示一个向量的坐标,通过计算
得到的结果的几何意义为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808c3ad4bf9b79102e5c163b88e298c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2cca094bab03a937ae77306b2d26cd.png)
A.关于y轴反射变换 | B.关于x轴反射变换 |
C.关于原点反射变换 | D.以上都不对 |
您最近一年使用:0次
3 . 关于矩阵乘法下列说法中正确的是( ).
A.不满足交换律,但满足消去律 | B.不满足交换律和消去律 |
C.满足交换律不满足消去律 | D.满足交换律和消去律 |
您最近一年使用:0次
4 . 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
5 . 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
6 . 已知
是
阶矩阵,
,则下列结论中错误的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777d8fccf0cf8b55a68488fe48b78744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 若
,则x的值是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35800b0af80e9f86009934f434cde220.png)
A.1 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知互不相同的三个实数
,则行列式
可能的值有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6369baf14f2546e49aedb0d6849d116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165bf04062dc8a7db237be9e2fe60f94.png)
A.3个 | B.4个 | C.5个 | D.6个 |
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9 . 设二元一次方程组为
若
,则
为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8011b9420a89321538e57a03c9ed1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37be5d6040ad6c396f724a8028f129b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858c3c4dc236e86e671b1c68798dfbdd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知
,
,若
,则
的值分别为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bcf191ba1227a50a05937f0c00b808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d95455f180bdd01a24ee5b9eb4ac2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
A.1,2 | B.2,![]() | C.2,1 | D.不存在 |
您最近一年使用:0次