What factors determine the direction of the resultant force vector? The overall aerodynamic force acting on a wing that is creating lift is not straight upward but is inclined backward. We usually consider the vertical and horizontal axes of the force separately. Lift is defined as the portion of the resultant force that is perpendicular to the relative wind, and induced drag is the portion parallel with it. The slope of the angle of the resultant force is the L/D ratio. This ratio changes with angle of attack as shown in the following diagram. As the AoA increases this vector leans further back creating a different L/D ratio (more drag for the same amount of lift).



Then looking from the wing's point of view, the portion of the RF perpendicular to the chord is the normal force (N) and the part parallel to it is the axial force (A). We can see that the the angle of the RF with respect to the wing chord is less affected by changes in AoA. 



I've never seen a chart that graphs out the N/A relationship. Does this ratio change at all with AoA or is it a fixed property of the wing design? If it is not fixed, what dynamic factors (speed, AoA, etc.) affect the direction of the resultant force?
Yes, the resulting force is not perpendicular to the wing's chord but can point either way, slightly forward and backward. The very first polar charts which were published show this nicely, because those plots were true polar plots and used the wing chord as the reference orientation for 0°.



Illustration on page 196 of Otto Lilienthal's "Der Vogelflug als Grundlage der Fliegekunst" showing measurements on model wings as polar plots (source). Note the left part: Here the forces are plotted in the wing section's coordinate system.

The N/A relationship was covered by the work of Edward C. Polhamus, who did a lot of research on this at NACA Langley and published several papers with equations for calculating the leading edge thrust, the force which helps to tilt the resultant force vector forward.