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The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is _________________.

- $10\hat{j}$
- $20\hat{i}$
- $-6\hat{i} - 6\hat{j}$
- $-4\hat{i} - 4\hat{j}$