A particle carrying a charge of \(+32.0 \mathrm{nC}\) is located at \((10.0 \mathrm{~nm}, 95. 0 \mathrm{~nm})\), and a particle carrying a charge of \(+98.0 \mathrm{nC}\) is located at \((45.0 \mathrm{~nm}, 56. 0 \mathrm{~nm})\). Calculate the electric force exerted on a charged particle placed at the origin if the charge on that particle is (a) \(3. 50 \mu \mathrm{C}\), (b) \(7.22 \mu \mathrm{C}\), (c) \(95.1 \mathrm{nC},(d)-77.5 \mathrm{nC}\),(e) \(1.00 \mathrm{mC}\), and \((f)\) 33. 2 C. (Once part \(a\) is done, there is a fast way to do this.)