The claim is, I can write any vector you give me as a real scale i plus a real scale j.

也就是说,我可以把任何你给我的矢量,写成 i 和 j 的实系数线性组合的形式

耶鲁公开课 - 基础物理课程节选

For the simplest context in which one can motivate a vector and also motivate the rules for dealing with vectors, is when you look at real space, the coordinates x and y.

对于最简单的情况,我们能用矢量,以及相关的规则来处理的,是实空间,x-y 坐标系

耶鲁公开课 - 基础物理课程节选