The problem is asking you to find a vector that is perpendicular to both [3 -1 2] and [2 0 1]. If you know how to find a cross product (and mr. fantastic has asked twice now if you do), that is the simplest thing to do. The cross product of two vectors is perpendicular to both.
If you do not, do you know that the two perpendicular vectors must have dotproduct equal to 0?
Write your vector as [a b c] and set the dot product of that with both [3 -1 2] and [2 0 1] equal to 0. That gives two equations for a, b, and c. That is not completely determined because there exist an infinite number of vectors perpendicular to two given vectors.