Thread: solution to vector in plane and their sum

I'm working on one of Gilbert Strang's exercises on vector subspaces. In the question, there is a vector x+y-2z=4. I need to find a solution and also their sum has to equal zero. I'm not sure if I understand the question:

Q: Let P be plane in with x+y-2z=4 and zero vector is not in P. Find 2 vectors in P and their sum must not be in P.

I assume that since their sum not in P, then the 2 vectors add to zero vector. I'm having trouble solving the equation to meet the requirements. How do I go about this?

Thanks

Well, if the sum were equal to zero, that would certainly work. But the sum could be any vector that's not in the plane, and you would have shown that the plane is not a vector subspace. Can you find two vectors in the plane? (Hint: try to find two non-collinear vectors).