Find the vector that is orthogonal to both u and v

u = (1,1,-2) and v=(2,-1,2)

I took the cross product and got (0,-6,-3)

What do I do now?

Assuming you calculated the cross product correctly, which I have not checked, the vector you have is orthogonal to the plane defined by u and v and a correct answer to the question posed. If you want, you could reduce it to a unit vector by dividing by the norm of the vector, 3√5.

Incidentally, the negative of the cross product is also a correct answer to the question asked.

What you do now is you look up the definition of a cross product. If you knew what it was, you would know you were done :)

Nothing more! That iself it normal to both given vector. Try takibg dot product of new vector with each of the given vectors.

I think that's it