## Calculating parallel vectors to paraboloid

Given the surface $\displaystyle z=2-x^2-y^2$, we need to find all vectors $\displaystyle (x,y,z)$ from the origin to the surface such that they are parallel to the normal at the point on the surface. Have determined the normal to be $\displaystyle (2u,2v,1)$ when we parameterize the surface as:
$\displaystyle r(u,v)=(u,v,2-u^2-v^2)$