Explain the position and displacement vectors for a particle moving in a plane using suitable equations.

(N/A) Position vector: The position vector $\vec{r}$ of a particle $P$ located in a plane with reference to the origin $O$ is given by:
$\vec{r} = x \hat{i} + y \hat{j}$
Where $x$ and $y$ are the components of $\vec{r}$ along the $x$ and $y$-axes,respectively,representing the coordinates of the object.
Displacement vector:
Suppose a particle moves along a curve and is at position $P$ at time $t$ and at position $P^{\prime}$ at time $t^{\prime}$.
At $P$,the position vector is $\vec{r} = x \hat{i} + y \hat{j}$.
At $P^{\prime}$,the position vector is $\vec{r}^{\prime} = x^{\prime} \hat{i} + y^{\prime} \hat{j}$.
The displacement vector $\Delta \vec{r}$ is the change in the position vector from $P$ to $P^{\prime}$:
$\Delta \vec{r} = \vec{r}^{\prime} - \vec{r}$
$\Delta \vec{r} = (x^{\prime} - x) \hat{i} + (y^{\prime} - y) \hat{j}$
$\Delta \vec{r} = \Delta x \hat{i} + \Delta y \hat{j}$
Where $\Delta x = x^{\prime} - x$ and $\Delta y = y^{\prime} - y$ are the changes in the $x$ and $y$ coordinates,respectively.