If two arrows are equal, you cannot be longer in the x direction and correspondingly short in the y direction.

如果要使两个矢量相等,那么即使 x 分量长一些,y 分量相应地小一些也是不行的

耶鲁公开课 - 基础物理课程节选

Unit vector i points away from the origin in the x direction.

单位矢量 i 从原点指向 x 轴正方向

耶鲁公开课 - 基础物理课程节选

I mentioned something of increasing importance only later, which is that you are free to pick another set of axes, not in the traditional x and y direction, but as an oblique direction.

后来我又讲了更重要的知识点,你可以随意选取另外一个坐标系,不再是传统的 x 和 y 方向,而是倾斜过的方向

耶鲁公开课 - 基础物理课程节选

It says, if you pull it to the right, so that x is positive, the spring will exert a force which is in the negative direction; that's why you have a minus sign.

就是说,如果你向右拉,x 取正值,弹簧产生的力方向为负,这就是这里用负号的原因

耶鲁公开课 - 基础物理课程节选

For most of us, gravity acts this way, defines a vertical direction very naturally and the blackboard is oriented this way, so very natural to call that x and call that y and line up our axes.

对我们多数人来说,重力作用下,很自然地确定了竖直方向,而我们的黑板又是这个指向的,所以很自然地定出 x 轴和 y 轴,并标出我们的坐标系

耶鲁公开课 - 基础物理课程节选