Vectors: planes, normals and distances

For the plane $x+2y+2z=6$, compare lines from the origin with directions $(2,-1,0)$ and $(1,0,0)$. Use dot products to predict whether each crosses the plane before substituting. Move the base point of the first line to $(6,0,0)$ without changing its direction and predict what changes. Explain how a contradiction, an identity and a single parameter solution represent the three geometric outcomes.