Vector Field Acting on a Curve

This Demonstration displays the principal components of a line integral. A point (black) moves along a parameterized curve (red) in a given vector field. The red vector is of unit length and lies tangent to the curve, the blue vector gives the field vector at the point's current location, and the green vector shows the field vector's projection on to the red arrow. The gray field vector lengths are only proportional to the magnitude of the field at that location, whereas the blue vector is exact.