Question: For the given vector field, find the divergence and curl of the field. a. (mathbf{F}=x mathbf{i}+y mathbf{j}) b. (mathbf{F}=frac{y}{r} mathbf{i}-frac{x}{r} mathbf{j}), for (r=sqrt{x^{2}+y^{2}}). c. (mathbf{F}=x^{2}
For the given vector field, find the divergence and curl of the field.
a. \(\mathbf{F}=x \mathbf{i}+y \mathbf{j}\)
b. \(\mathbf{F}=\frac{y}{r} \mathbf{i}-\frac{x}{r} \mathbf{j}\), for \(r=\sqrt{x^{2}+y^{2}}\).
c. \(\mathbf{F}=x^{2} y \mathbf{i}+z \mathbf{j}+x y z \mathbf{k}\).
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