f=3xyi−5zj+10xkdivf=∇.Fwhere ∇=∂∂xi + ∂∂yj + ∂∂zkF=∂∂x3xy−∂∂y5z+∂∂z10x=3ycurlF=∇∗F=∣ijk∂∂x∂∂y∂∂z3xy−5z10x∣=5i−10j−3xkf = 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-3xkf=3xyi−5zj+10xkdivf=∇.Fwhere ∇=∂x∂i + ∂y∂j + ∂z∂kF=∂x∂3xy−∂y∂5z+∂z∂10x=3ycurlF=∇∗F=∣∣i∂x∂3xyj∂y∂−5zk∂z∂10x∣∣=5i−10j−3xk
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