1.12.1 Vector analysis

Problem: Find the gradient of the scalar field \( u(x, y, z)= \) \( z e^{x^{2}+y^{2}+z^{2}} \) at an arbitrary point and at the point \( M_{0}(0,0,0) \). For the resulting vector field \( \bar{a}= \) \( \Delta u(x, y, z) \) find \( \operatorname{div} \bar{a} \) and \( \operatorname{rot} \bar{a} \) at the point \( M_{0} \).