My math book tells me the equation for a flux integral over a cylinder for instance is the integral(over the region) of the force vector field in terms of R, theta, and z, dotted with cos(theta)ihat+sin(theta)jhat, multiplied by R, dzdtheta.

That is all great when the force vector field given is in terms of ihat, jhat, and khat. However, my homework has force vector fields in terms of rhat, thetahat, and zhat, or for spherical roehat, thetahat, phihat.

So I don't know how to either change my force vector field from r,theta,z to x,y,z (in polar terms) or to change what I'm supposed to dot it with to r,theta,z coordinates.

One of the problems: Calculate the flux of the vector field F=(4roe^2)thetahat through the surface of the sphere centered on the origin with radius 4

How to I change 4roe^2thetahat to an i, j, k vector that I can dot with cos(theta)ihat+sin(theta)jhat, or change cos(theta)ihat+sin(theta)jhat to a roe, theta, phi vector that I can dot with 4roe^2thetahat?

Sorry that was so long. I am desperate for help, though, and any is very much appreciated.