(Solved): Problem 1.15 Calculate the divergence of the following vector functions: (a) \( \mathbf{v}_{a}=x^{2 ...

Problem 1.15 Calculate the divergence of the following vector functions: (a) \( \mathbf{v}_{a}=x^{2} \hat{\mathbf{x}}+3 x z^{2} \hat{\mathbf{y}}-2 x z \hat{\mathbf{z}} \). (b) \( \mathrm{v}_{b}=x y \hat{\mathbf{x}}+2 y z \hat{\mathbf{y}}+3 z x \hat{\mathbf{z}} \). (c) \( \mathbf{v}_{c}=y^{2} \hat{\mathbf{x}}+\left(2 x y+z^{2}\right) \hat{\mathbf{y}}+2 y z \hat{\mathbf{z}} \)