What does it mean for a vector to be perpendicular or lie on a Plane?

Question

Is one of two question/answer false?

1. Finding the vector perpendicular to the plane (see accepted answer)
2. https://nbviewer.jupyter.org/github/mitmath/1806/blob/master/psets/pset2sol.ipynb (Q1 last part)

In a nutshell: w is vector perpendicular to plane. 1 says any vector on plane is perpendicular to w. 2 says to find a vector on plane in direction of w.