Actually, the view of vectors we take nowadays is that vectors are associated with a pair of numbers which, on the rotation of axes, transform like this.

实际上,今天我们讲矢量所用的观点是,矢量是和一组坐标值相对应的,在坐标轴旋转的过程中像这样变换

耶鲁公开课 - 基础物理课程节选

This seems to work for vectors.

这在矢量运算中仍然适用

耶鲁公开课 - 基础物理课程节选

You've got to be very used to the notion of taking a vector in some oblique direction and writing it in terms of i and j.

你们应该已经很熟悉,倾斜的坐标系中矢量的概念,和用 i 和 j 来表示该矢量的方法

耶鲁公开课 - 基础物理课程节选