Answer
The equation in rectangular coordinates: $2x-z=0$
Work Step by Step
We have $z = 2r\cos \theta $.
In cylindrical coordinates we have $x = r\cos \theta $. So, $z = 2r\cos \theta $ becomes $z=2x$ in rectangular coordinates. We may write this equation as
$2x-z=0$
By Theorem 1 of Section 13.5, this is the equation of a plane with normal vector $\left( {2,0, - 1} \right)$ (red arrow in the second figure).
