# Problem: Consider the given vector field. F(x, y, z) = (x + yz)i + (y + xz)j + (z + xy)k (a) Find the curl of the vector field. (b) Find the divergence of the vector field.

###### FREE Expert Solution

Curl:

Divergence:

$\overline{){\mathbf{\nabla }}{\mathbf{•}}{\mathbf{F}}\begin{array}{ccc}\mathbf{=}\mathbf{\left(}\frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{x}}\stackrel{\mathbf{^}}{\mathbf{i}}\mathbf{,}& \frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{y}}\stackrel{\mathbf{^}}{\mathbf{j}}\mathbf{,}& \frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{z}}\stackrel{\mathbf{^}}{\mathbf{k}}\end{array}{\mathbf{\right)}}{\mathbf{F}}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{,}}{\mathbf{y}}{\mathbf{,}}{\mathbf{z}}{\mathbf{\right)}}}$

###### Problem Details

Consider the given vector field. F(x, y, z) = (x + yz)i + (y + xz)j + (z + xy)k

(a) Find the curl of the vector field.

(b) Find the divergence of the vector field.