If I want to draw the lines of force to a vector field F and consider whether any results are physically reasonable, then i can start with to solve the differentiable equation
$$ y'(x)= {F_y(x,y) \over F_x(x,y)} $$
When I solve this differentiable eqution then I will find out the integral curve for the vector field. But how do I find out the field direction and "strength" for the vector field?? And if the i am taking the integral of avector field over a curve p $$(1) \int_p F*dr$$ and if this curve p is orthogonal against the integral curve of the vectorfield, then the result of the integral (1) will be zero, right?