If two vectors are parallel then any vector that is orthogonal to one is orthogonal to the other. And, in three dimensions, there exist an infinite number of vectors orthogonal to a given vector. If the given vector is <a, b, c> then <x, y, z> is orthogonal to it as long as ax+ by+ cz= 0. Choose any value for any two of x, y, and z and solve for the other.