Skip to main content Contents Index Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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Section 1.14 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 1.20 . It is important to note that the position vector depends not only on the given point, but also on the choice of origin.
Figure 1.20. The position vector corresponding to the point \(P\text{.}\)
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{1.14.1}
\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 $P$.
