Express Coulomb's law in vector form in terms of `r_(12)`

Explanation

Coulomb.s law in vector form in term of `r_(12)`
Here `r_(1) = OA = ` position vector of `q_(1) , r_(2) = OB`= position vector of `q_(2)` Vector pointing from `q_(1)` to `q_(2)`

`AB = r_(12) = r_(2) - r_(1)`
Similarly vector pointing from `q_(2)` to `q_(1)` is `AB = r_(21) = r_(1) - r_(2)`
Now , `|r_(12)| = r_(12)` and `|r_(21)| = r_(21)`
`therefore hatr_(12) = (r_(12))/(f_(12))` and `hatr = (r_(21))/(f_(21))`
Let `F_(12)` = force on `q_(1)` due to `q_(2)` and `F_(21)` = force on `q_(2)` due to `q_(1)`
Coulomb.s force between two point charges `q_(1)` and `q_(2)` located at `r_(1)` and `r_(2)` in vacuum is expressed as
`F_(21) = (1)/(4 pi epsi_(0)) (q_(1) q_(2))/(AB^(2))` along AB
As , `F_(21) = (1)/(4 pi epsi_(0)) (q_(1) q_(2))/(r_(12)^(2)) "" hatr_(12)`