What is a position vector? What is a displacement vector? Explain the equality of vectors.

(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. $\overrightarrow{OP}$ 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 $t^{\prime}$).
Equality of vectors: Two vectors $\vec{A}$ and $\vec{B}$ are said to be equal if and only if they have the same magnitude and the same direction.
Figure $(a)$ shows two equal vectors $\vec{A}$ and $\vec{B}$. We can easily check their equality by shifting $\vec{B}$ parallel to itself until its tail $Q$ coincides with that of $\vec{A}$ (i.e.,$Q$ coincides with $O$). Then,their tips $S$ and $P$ also coincide. The two vectors are then said to be equal,denoted as $\vec{A} = \vec{B}$.