Explain position and displacement vectors. How is the magnitude of a vector quantity represented?

(N/A) Position vector: To describe the position of an object moving in a plane,we need to choose a convenient point,say $O$,as the origin.
Let $P$ and $P^{\prime}$ be the positions of the object at time $t$ and $t^{\prime}$,respectively,as shown in figure $(a)$. $\overrightarrow{OP}$ is the position vector of the object at time $t$. It is represented by the symbol $\vec{r}$.
Point $P^{\prime}$ is represented by another position vector,$\overrightarrow{OP^{\prime}}$,denoted by $\vec{r}^{\prime}$.
The length of the vector $\vec{r}$ represents the magnitude of the vector,and its direction is the direction in which $P$ lies as seen from $O$.
Displacement vector: If the object moves from $P$ to $P^{\prime}$,the vector $\overrightarrow{PP^{\prime}}$ (with the tail at $P$ and the tip at $P^{\prime}$) is called the displacement vector corresponding to the motion from point $P$ (at time $t$) to point $P^{\prime}$ (at time $t^{\prime}$).
Important notes:
$(1)$ The displacement vector is the straight line joining the initial and final positions.
$(2)$ It does not depend on the actual path taken by the object between the two positions. For example,in figure $(b)$,given the initial and final positions as $P$ and $Q$,the displacement vector is the same $\overrightarrow{PQ}$ for different paths of the journey,such as $PABCQ$,$PDQ$,and $PBEFQ$.
$(3)$ Therefore,the magnitude of displacement is always less than or equal to the path length of an object between two points.