1 . 已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d2051594370095e72e173fd95888a.png)
是空间的一组基,则向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a951d98b418b737673d2544d02e90e.png)
也是空间的一组基;
( )
2022-03-08更新
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121次组卷
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2卷引用:习题 3-3(已下线)习题 3-3(已下线)第02讲 空间向量基本定理(5大考点8种解题方法)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
2 . 判断下列命题的真假:
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
共线,则向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
所在的直线平行
( )(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
所在的直线是异面直线,则向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
一定不共线
( )(3)若三个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
两两共面,则三个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
一定共面
( )(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
是空间三个向量,则对空间任一向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
,总存在唯一的有序实数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b525d8c768efd801ab58bc4c0da9221e.png)
,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81b46a3ddb3f2b793df6294d710bab1.png)
.
( )
2021-12-04更新
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164次组卷
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1卷引用:6.2空间向量的坐标表示