If you don't know cross product then understanding dot products can help to figure out another way (which is what you probably did):
(a,b,c) * (1,2,3) = 0
(a,b,c,) * (-1,-1,1) = 0
where (a,b,c) is perpendicular to both specified vectors.
That gives this matrix,
.1 2 3 | 0
-1-1 1 | 0...