The potential energy for a force field \(\vec{F}\) is given by :

\(U(x, y) = \cos ({x+y})\)

The force acting on a particle at position given by coordinates (0, π/4) is :

\(\frac{1}{\sqrt{2}} (\hat{i} + \hat{j})\)

\(F_x = -\frac{\delta U}{\delta x} = \sin ({x+y}) = \frac{1}{\sqrt{2}}\)

\(F_y = -\frac{\delta U}{\delta y} = \sin ({x+y}) = \frac{1}{\sqrt{2}}\)

\(\vec{F} = \frac{1}{\sqrt{2}} (\hat{i} + \hat{j})\)