Find two unit vectors each of which is perpendicular to vectors (1, 1, 0) and (1,0,1)

What I did:
a x b = (1, -1, -1)
|axb|=square toot 3

correct answer is +/- (1/√3 - 1/√3 - 1/√3)
or
=+/- 1/√3 (1, -1, -1)