在学习计算位移之前，让我们先定义位移，然后学习什么是位置向量以及如何编写它。

位移的定义

位移是对粒子初始位置和最终位置之间差异的测量。它是运动学中使用的基本量之一，也用于导出速度和加速度。位移是一个向量量，它有一个量值（大小）和一个方向。要计算位移，需要从最终位置的位置向量中减去初始位置的位置向量。所以，在讨论位移之前，理解位置是如何用向量表示的是很重要的。

什么是位置矢量(position vector)？

A position vector gives the position of a particle with respect to the origin of the coordinate system. In our discussion, we will limit ourselves to a system of 3-dimensional Cartesian coordinates. The position vector for a particle  at coordinates ,  .

如何计算位移

Suppose a particle moves from a point  , that has a position vector  to a new position  with a position vector position vector  . Then the displacement vector is given by  .

例子

A particle moves from position  to  . Calculate displacement vector for this motion.

We have  and  . Therefore,  .

如何计算净位移

Suppose a particle moves several times. The net displacement is the displacement vector between the particle’s initial position and the final position. The net displacement can also be obtained by vector addition of each of the individual displacement vectors that corresponds to each stage of motion. For example, in the diagram below, the position vector of the point is and the position vector of  the point is . Then, the net displacement  .

如何计算位移量

As mentioned earlier, displacement is a vector quantity. The magnitude (size) of this vector quantity gives the distance. If the displacement vector  , then the magnitude  is given by  .

In the earlier example, we had a displacement vector of  . The magnitude of this vector is  .