名校
1 . 空间中,两两互相垂直且有公共原点的三条数轴构成直角坐标系.如果坐标系中有两条坐标轴不垂直,那么这样的坐标系称为“斜坐标系”.现有一种空间斜坐标系,它任意两条数轴的夹角均为
,我们将这种坐标系称为“斜
坐标系”.我们类比空间直角坐标系,定义“空间斜
坐标系”下向量的斜
坐标:
分别为“斜
坐标系”下三条数轴(
轴,
轴,
轴)正方向上的单位向量,若向量
,则
与有序实数组
一一对应,称向量
的斜
坐标为
,记作
.
(1)若
,求
的斜
坐标;
(2)在平行六面体
中,
,建立“空间斜
坐标系”如下图所示.
①若
,求向量
的斜
坐标;
②若
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4664eed9e1abab0ed6397c58d70e731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.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/138c39673b579f1346c38398811105a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee4e3cf72016a2b908b9178b8317b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee4e3cf72016a2b908b9178b8317b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971975007772deb92f837127a7936389.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fe31c74115f017c61dc7e6d78d5fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
(2)在平行六面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96b1713aa3c420848e9865afefa3fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/27/30f606bc-c728-4798-a6d6-a33bb22e85bf.png?resizew=181)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099edd3520292558184521a9af4e9064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253b99b8c8a45ace50b590cdd89b238a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcc897340d513ba62e60b02e5ede30a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cbb23e8edee78010195fe66d3e55b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5813dd9f2bd01a38d749247eccca5449.png)
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3卷引用:湖北省宜荆荆随2023-2024学年高二上学期10月联考数学试题
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解题方法
2 . 如图,在长方体
中,
,
,点M在棱
上,且
,则当
的面积取得最小值时其棱![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9f23207b67eba6a74de672076c946b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df998ca31abcbdccb3e43f6269b80702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e1be72811a16954505eee3ee7a291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9f23207b67eba6a74de672076c946b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/1802bb16-a22a-4c30-9e66-52de1f9392d6.png?resizew=127)
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7卷引用:湖北省武汉情智学校2023-2024学年高二上学期10月质量检测数学试题
湖北省武汉情智学校2023-2024学年高二上学期10月质量检测数学试题四川省南充市2019-2020学年高二(下)期末数学(理科)试题海南省儋州市第一中学2020-2021学年高二上学期第一次月考数学试题(已下线)1.1.1 柱、锥、台、球的结构特征-2020-2021学年高一数学课时同步练(人教A版必修2)(已下线)1.3 空间向量及其运算的坐标表示(精练)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)广东培才高级中学2023-2024学年高二上学期10月月考数学试题安徽省六安市舒城县晓天中学2023-2024学年高二上学期第一次月考数学试题
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3 . 在空间直角坐标系
中,已知平面
的一个法向量是
,且平面
过点
.若
是平面
上任意一点,则点
的坐标满足的方程是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842b92306592be408750ff6e1d455da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aba57b36e4e16a7a2c009b652b1989c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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