Let [tex]x = 3\cos(t)[/tex] and [tex]y=3\sin(t)[/tex]. Then
[tex]z = xy = 9\cos(t)\sin(t) = \dfrac92 \sin(2t)[/tex]
So we can parameterize the intersection by
[tex]\vec r(t) = 3\cos(t)\,\vec\imath + 3\sin(t)\,\vec\jmath + \dfrac92 \sin(2t)\,\vec k[/tex]
with [tex]0\le t\le2\pi[/tex].
