Three charges are arranged in space as shown below. Charge $q_1=+2\mathrm{.}75C$ is located at the origin, charge $q_2=-1\mathrm{.}25C$ is located a distance of $r_{12}=0\mathrm{.}125m$ at an angle of ${}_1=25$ and charge $q_3=+3\mathrm{.}15C$ is located a distance of $r_{13}=30.$ For this arrangement, we are looking at the net forces that would act on charge $q_1.$

$($a$)$ Draw the force diagram of the forces acting on charge $q_1.$

$($b$)$ Calculate the $x-$ and $y-$components of the force between charges $q_1$ and $q_2.$

$($c$)$ Calculate the $x-$ and $y-$components of the force between charges $q_1$ and $q_3.$

$($d$)$ Calculate the net force acting on charge $q_1.$

$($e$)$ Calculate the direction of the net force acting on charge $q_1.$ Remember to present this appropriately.