Finding a vector parallel to a plane

[stratusfactio]

Homework Statement

Just a general question for studying purposes. How do you find a vector parallel to a plane?

Let's say that we have a plane $$2x-3y-z=0$$...I know that the perpendicular vector to this plane is $$<2,-3,-1>$$ but how do I use this information to determine a parallel vector?

 

[Bacle]

Well, you know of a vector that forms a right angle, i.e., is perpendicular to, the plane, so how would you find vectors that are perpendicular to the perpendicular?

O.K, it's a mouthful. Consider a plane parallel to 2x-3y-z=0. What would be its equation? Remember the perspective of a plane as a set of vectors perpendicular
to a given fixed vector.