Section 3.14 The Position Vector
The position vector \(\rr\) is the displacement vector that points from the origin to a given point \(P\text{,}\) as shown in Figure 3.14.1. It is important to note that the position vector depends not only on the given point, but also on the choice of origin.
As with any vector, we can express the position vector in terms of a basis. In rectangular coordinates, the position vector is given by
\begin{align}
\rr
&= r_x\,\xhat + r_y\,\yhat + r_z\,\zhat\notag\\
&= x\,\xhat + y\,\yhat + z\,\zhat\tag{3.14.1}
\end{align}
since the components \(\{r_x,r_y,r_z\}\) of the position vector are just the rectangular coordinates \((x,y,z)\) of the point $P$.