Displacement Of a particle moving along a curve in a plane:

Let us consider a point A in a two-dimensional Cartesian co-ordinate system, the position of this point can be described by a specific single vector. This vector is the displacement of that point A with respect to the origin O of the co-ordinate system, as shown in the figure below.

This vector is known as the “position vector” of that point A with respect to the origin O.

Here the position vector is denoted by the \( \vec{OA}=\vec{r} \).

\( \vec{r} \) gives the magnitude as well as the direction of displacement.

If \( \hat{r} \) be the unit vector along \( \vec{r} \), then we can write,

\( \displaystyle{\hat{r}=\frac{\vec{r}}{|\vec{r}|}} \). where, \( |\vec{r}| \) is the magnitude of the vector \( \vec{r} \).