I have a normal vector (2,-2,0) of the a plane and a point on a line orthogonal to the plane, (4,0,1). So my goal is to try and find the parametric description of this line.

now to do that I need a vector v, but how can I find this vector with the given info?

the parametric representation is given by p + tv where p is a point and v is a vector. I need another point on this line to find the vector. Since this line is orthogonal to the plane I know that this vector should be parallel to the normal vector of the plane. But im having difficulty trying to find another point on this line.