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 $\displaystyle \mathbb{R}^2$ 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