I understand how to calculate a vector cross product. I also understand that in order to calculate a vector cross product we are calculating the determinant of a 3 x 3 matrix. I guess I have a few questions. 1)How did mathematicians or physicists discover how to calculate the determinant of a 3 x 3 matrix, and what does this determinant represent? For example, A x B = (AyBz - ByAz)i - (AxBz-BxAz)j + (AxBy-BxAy)k. 2) How did we know to put a negative in front of the j term? 3) How did we recognize that phenomena like Torque and Magnetic Force could be described by cross products? I hope that I am being clear enough and don't sound like a confused idiot. I'd appreciate answers to any of these questions.