Find two nonparrallel vectors both orthogonal to (1,1,1)

[sigma]

Find two nonparrallel vectors both orthogonal to (1,1,1)

So I set up a dot product with a blank vector and (1,1,1) and equated it to 0 (because the dot product = 0 means its orthogonal) so I had something like this

(_,_,_) . (1,1,1) = 0

and I just plugged in numbers that would make 0=0 so

(0,-1,1) . (1,1,1) = 0
0=0

so thats one vector thats orthogonal to (1,1,1). To find the other one do I just do the same but change the order of the vector? Because (-1,1,0) or (1,-1,0) or (1,0,-1) etc would work so do I just pick any one along with (0,-1,1) and that would be my 2 nonparrallel vectors?

 

[pka]

Any two of these will work: \(\displaystyle \left\langle {1,0, - 1} \right\rangle ,\;\left\langle {1, - 1,0} \right\rangle ,\;\left\langle {0,1, - 1} \right\rangle .\)