# Vectors parallel to plane, perpendicular to another vector

From Anton, I have this simple looking LA question:

Find all unit vectors parallel to the yz plane that are perpendicular to the vector 3,1,-2

Since this vector is sloped in all 3 dimensions, and since yz is I flat in the x dimension, I am baffled how this can have a solution.

I found a near exact version of this question on another forum but the vector given did have a zero component.

I'm clearly missing some obvious detail, a quick point out would be much appreciated.

Any vector in the $i$ direction is perpendicular to the yz plane. So you need a vector perpendicular both to $i$ and the vector $<3,1,-2>$. How do you find a vector perpendicular to two given vectors?