I've posted this question twice, the first time I accidentally typed the problem wrong and I don't know what he did anyway. The second time the answerer left off right where I originally got stuck. If someone could help me with a solution to this, I would be very grateful

Find all the vectorsu that satisfy the equation <1,1,1> X u = <0,0,1>

I don't know if there are multiple ways of doing this, but we're using the determinant!

(The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)