Question

State Coulomb's law and express it in vector form.

Answer 1

Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other. In its scalar form, the law is:
where ke is Coulomb's constant (ke ≈ 9×109 N m2 C−2), q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).

he vector form of Coulomb's law is simply the scalar definition of the law with the direction given by the unit vector, r̂21, parallel with the line from charge q2 to charge q1.[15] If both charges have the same sign (like charges) then the product q1q2 is positive and the direction of the force on q1 is given by r̂21; the charges repel each other. If the charges have opposite signs then the product q1q2 is negative and the direction of the force on q1 is given by −r̂21 = r̂12; the charges attract each other.

Answer 2

coulomb's law
F=Kq1q2/r^2
to write it in vector form we will multiply it with unit vector of r. (let R be the unit vector)
=kq1q2R/|r|
|r|=magnitude of r vector