Halliday, Resnick & Walker — Coulomb's Law: Problem 23

23 The charges and coordinates of two charged particles held fixed in an xy plane are $q_1 = +3.0 \text{ \mu C}$, $x_1 = 3.5 \text{ cm}$, $y_1 = 0.50 \text{ cm}$, and $q_2 = -4.0 \text{ \mu C}$, $x_2 = -2.0 \text{ cm}$, $y_2 = 1.5 \text{ cm}$. Find the (a) magnitude and (b) direction of the electrostatic force on particle 1 due to particle 2. At what (c) x and (d) y coordinates should a third particle of charge $q_3 = +6.0 \text{ \mu C}$ be placed such that the net electrostatic force on particle 1 due to particles 2 and 3 is zero?