Given equation of the plane is $z=2$
This can be written as $0x+0y+z=2$------(1)
Hence the direction ratios of the normal are $(0,0,1)$
Dividing LHS and RHS of eq(1) by 1,we get
This is of the form $lx+my+nz=d$,where $l,m,n$ are the direction cosines of the normal to the plane and $d$ is the distance of the perpendicular drawn from its origin.
Therefore the direction cosines are $0,0$ and $1$ and the distance from the origin is 2 units.