The number of vectors of unit length perpendicular to any two vectors is_?
Assuming that the two vectors are not scalar multiples of one another, the two vectors determine a plane. The normal vector to that plane is one of the two unit vectors. One finds the normal vector by taking the cross-product of the two original vectors.
After finding the perpendicular vector, scale it to unit length. That vector, N, is one of the two. The other vector is -N -- the perpendicular vector in the opposite direction to N.