But this expression right over here we're taking a line integral we care specifically about the points about along this curve along this contour right over here and so lets think about what this is actually this piece right over here is actually telling us before we sum up all of these infinitesimally small pieces so if we just take f dot n so lets just think about a point on this curve so a point on this curve may be this point right over here so associated with that point there is a vector that's what the vector field does