In my textbook there is a question where they ask for a basis for the 1x3 matrix:

(10 20 10)

Answer: an orthogonal basis is {(-1,0,1)^T,(1,-1,1)^T}.

So, I know that the equation corresponding to the homogeneous system would be "10x+20y+10z=0", but I can't see how to solve this to get that basis. Could anyone please show me how we can get that answer?