$*15$ The charges and coordinates of two charged particles held fixed in an $xy$ plane are $q_1=+3\mathrm{.}0C,x_1=3\mathrm{.}5cm,y_1=0\mathrm{.}50cm,$ and $q_2=-4\mathrm{.}0C,x_2=-2\mathrm{.}0cm,y_2=1\mathrm{.}5cm.$ Find the $($a$)$ magnitude and $($b$)$ direction of the electrostatic force on particle $2$ due to particle $1.$ At what $($c$)x$ and $($d$)y$ coordinates should a third particle of charge $q_3=+4\mathrm{.}0C$ be placed such that the net electrostatic force on particle $2$ due to particles $1$ and $3$ is zero?