I tie a spring to my back and I anchor it to the wall and see how much the spring stretches before the two forces balance.

我把弹簧一端系在背后,另一端固定在墙上,观察两个力平衡时弹簧的伸长量

耶鲁公开课 - 基础物理课程节选

So multiplying a vector by a number means stretch it by that factor.

所以用数字乘以矢量,就相当于将它伸长了相应的倍数

耶鲁公开课 - 基础物理课程节选

We know that because you can stretch i by whatever factor you like.

因为你可以让 i 伸长任意的倍数

耶鲁公开课 - 基础物理课程节选

It also tells you that if you compress the spring, compress it means x is now-- x is measured from this position, where the spring is neither compressed nor expanded.

它还能告诉你,如果压缩弹簧,压缩就意味着现在 x...,x 是从这个位置开始算的,在这个位置弹簧既没有压缩也没有伸长

耶鲁公开课 - 基础物理课程节选