To find the magnitude of a force between two charges is very simple, but to get the direction of the force seems a little strange to me. The signs of the charges aren't included anywhere in the law, so does this mean that I literally have to think "the signs are opposite, therefore I will multiply the vector by -1 (or leave it positive, depending on my reference coordinates)"? This seems a little bit cumbersome and forced to me, and apparently not derived anywhere in the mathematics of it. Am I going about doing this the right way? I'm quite accustomed with vectors (vector calculus and linear algebra background), but very new to e&m. Any help would be much appreciated.