Line integrals of vector fields-positive, negative, or zero I have a question about line integrals of vector fields being positive, negative, or zero. If you are measuring the work it takes to "push" a point on the curve through the vector field, does this mean that going in the same direction is negative, opposite direction is positive, and perpendicular is zero? 
Someone please correct me if I'm wrong. 

The line integral measures the amount of work done by the vector field (representing a force field) in order to move a particle along the curve. So it is not work done against the vector field, but rather by the vector field that is being measured. Hence when the tangent to the curve points in the same direction of the vector field, the integral is positive.
