You are given three charged particles. Particles 1 and 2 carry charge \(+q\) and particle 3 carries charge \(-4 q\).

(a) Determine the relative values of the separation distances \(r_{12}\) and \(r_{13}\) when the three particles are arranged along a straight line in such a way that the vector sum of the forces exerted on particle 1 is zero.

(b) With the particles arranged this way, are the vector sums of the forces exerted on particles 2 and 3 also zero?