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The potential energy for a force field \( \vec{F} \) is given by \( \mathrm{U}(\mathrm{x}, \mathrm{y})=\cos (\mathrm{x}+\mathrm{y}) \). The force acting on a
\( \mathrm{P} \) particle at position given by coordinates \( \left(0, \frac{\pi}{4}\right) \)

W is
\( -\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}) \)
(2) \( \frac{1}{\sqrt{2}}(\hat{i}+\hat{j}) \)
(3) \( \left(\frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j}\right) \)
(4) \( \left(\frac{1}{2} \hat{\mathrm{i}}-\frac{\sqrt{3}}{2} \hat{\mathrm{j}}\right) \)
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