**Coulomb's Law in Vector Form**

Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law can be expressed in vector form as:

**F = (k * q1 * q2) / r^2 * r̂**

Where,
- F = Force between two charged objects
- q1 and q2 = Magnitudes of the charges on the two objects
- r̂ = Unit vector pointing from q1 to q2
- r = Distance between the two charged objects
- k = Coulomb's constant

**Explanation of the Equation**

- The magnitude of the force between two charged objects is directly proportional to the product of their charges. This means that if one of the charges is increased, the force between them will increase as well.
- The magnitude of the force between two charged objects is inversely proportional to the square of the distance between them. This means that as the distance between the two charged objects increases, the force between them will decrease.
- The unit vector r̂ points from q1 to q2. This is important because it indicates the direction of the force. If the two charges are of the same sign, the force will be repulsive and the unit vector will point away from q2. If the two charges are of opposite signs, the force will be attractive and the unit vector will point towards q2.
- Coulomb's constant k is a proportionality constant that depends on the units of the charges and distance. Its value is approximately 9 x 10^9 Nm^2/C^2.

**Conclusion**

Coulomb's law is an important concept in the study of electromagnetism. It helps us understand how charged objects interact with each other and how to calculate the force between them. The vector form of Coulomb's law is particularly useful because it gives us both the magnitude and direction of the force.