List of top Geophysics Questions on Vector Calculus

Given Vector Field:

\[ \vec{A} = (bx+4y^2z)\hat{i} + (x^3\sin z-3y)\hat{j} - (e^x+4\cos(x^2y))\hat{k} \]

For a vector field to be solenoidal,

\[ \nabla \cdot \vec{A}=0 \]
 

The equation of right circular cylinder of radius \(2\ \text{cm}\) whose axis passes through the point \((1,2,3)\) and has direction cosines proportional to \((2,-3,6)\) is:
Evaluate \(\iint_S \vec{A}\cdot \hat{n}\,dS\), where \(\vec{A}=2y\hat{i}+yz\hat{j}+xz\hat{k}\) and \(S\) is the surface of the region bounded by \(x=0,\ y=0,\ z=0,\ y=3\) and \(x+2z=6\).