Answer to Question #229583 in Calculus for Rohan

Question

Find the divergence and curl of the f=3xyi-5zj+10xk

Answer 1

$f = 3xyi -5zj+10xk \\divf= \nabla .F \\\text{where $\nabla = \frac{\partial}{\partial x}i$ + $\frac{\partial}{\partial y}j$ + $\frac{\partial}{\partial z}k$} \\F= \frac{\partial}{\partial x}3xy - \frac{\partial}{\partial y}5z + \frac{\partial}{\partial z}10x \\=3y \\curl F = \nabla * F \\ = \begin{vmatrix}i&j&k\\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z}\\ 3xy & -5z & 10x \end{vmatrix} \\= 5i-10j-3xk$