Order of addition

If we are adding two force vectors, F + G, is it valid to assume as in ordinary algebra that F + G is the same as G + F?

To tell if this algebra rule also applies to vectors, we simply translate the vector notation into ordinary algebra notation. In terms of ordinary numbers, the components of the vector F+G would be F_x +G_x , F_y +G_y , and F_z + G_z , which are certainly the same three numbers as G_x + F_x , G_y + F_y , and G_z + F_z . Yes, F + G is the same as G + F.