Hello Mathematicians! I have the answer to a very simple problem, but I dont understand it.

Following vector field is given:

G(x,y,z) = (x - yz, y+xz, z)

I am asked to write the representation

**Ĝ**(r, fi, z) of the given field in cylindrical coordinates (where fi is the angle).

So here´s what I wrote:

**Ĝ(r, fi, z)**= ( r( cos(fi)-zsin(fi) ) , r( sin(fi) + zcos(fi) ) , z ) I just substituted x= rcos(fi) and y=rsin(fi)

But this is the answer that comes in the answers paper:

**Ĝ(r, fi, z)** = (r , zr, z) Doesnt make any sense to me... Could it be a mistake in the solutions paper?

Could someone explain why the answer is so, and why what I wrote is wrong?

Thanks!!