Explain the vector form of Coulomb's law and its importance. Write some important points regarding the vector form of Coulomb's law.

(N/A) Consider two point charges $q_{1}$ and $q_{2}$ at positions $\vec{r}_{1}$ and $\vec{r}_{2}$ respectively,as shown in figure $(a)$.
Let $\vec{F}_{12}$ be the force on $q_{1}$ due to $q_{2}$,and $\vec{F}_{21}$ be the force on $q_{2}$ due to $q_{1}$.
The displacement vector from $q_{1}$ to $q_{2}$ is $\vec{r}_{21} = \vec{r}_{2} - \vec{r}_{1}$,and from $q_{2}$ to $q_{1}$ is $\vec{r}_{12} = \vec{r}_{1} - \vec{r}_{2} = -\vec{r}_{21}$.
The unit vectors are $\hat{r}_{21} = \frac{\vec{r}_{21}}{|\vec{r}_{21}|}$ and $\hat{r}_{12} = \frac{\vec{r}_{12}}{|\vec{r}_{12}|}$.
According to Coulomb's law in vector form:
Force on $q_{2}$ due to $q_{1}$ is $\vec{F}_{21} = \frac{1}{4 \pi \epsilon_{0}} \frac{q_{1} q_{2}}{r_{21}^{2}} \hat{r}_{21}$.
Force on $q_{1}$ due to $q_{2}$ is $\vec{F}_{12} = \frac{1}{4 \pi \epsilon_{0}} \frac{q_{1} q_{2}}{r_{12}^{2}} \hat{r}_{12}$.
Since $\hat{r}_{12} = -\hat{r}_{21}$ and $r_{12} = r_{21}$,we get $\vec{F}_{21} = -\vec{F}_{12}$.
Importance and important points:
$1$. It shows that electrostatic force obeys Newton's third law of motion.
$2$. It indicates that the force acts along the line joining the two charges (central force).
$3$. It accounts for both magnitude and direction of the force.