It comes from the fact that velocity is a vector and you can change your velocity vector by changing your direction.

其原理就是,速度是矢量,你可以通过改变方向来改变速度

耶鲁公开课 - 基础物理课程节选

But I know when I multiply a vector by a number, I get a vector in the same direction.

但是我所知道的是当矢量乘以一个常数,我会得到一个同方向的矢量

耶鲁公开课 - 基础物理课程节选

We learned that a vector is a quantity that has a magnitude and a direction.

我们已经知道矢量是一个,既有大小又有方向的量

耶鲁公开课 - 基础物理课程节选

It's good to have a vector pointing in the radial direction of length one.

所以引入这么一个模长为 1,方向沿圆心向外辐射的矢量作用很大

耶鲁公开课 - 基础物理课程节选

This is the reason behind saying a vector has a magnitude and a direction.

这就是矢量既有大小也有方向的原因

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The fact that when you go in a circle, you accelerate is what we're learning here, coming from the fact that velocity is a vector and its change can be due to change in the magnitude or change in direction.

而当你做圆周运动时你也在加速,这是我们在这里所学到的,原因就在于,速度是一个矢量,其变化可以通过改变模长,或者方向来实现

耶鲁公开课 - 基础物理课程节选

At each point, er is a different vector pointing in the radial direction of length one.

矢量 er 在每一点处都不同,方向都从圆心指向该点,模长为1

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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

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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