Calculus 3 Question

[Xibalba]

I want to know how you tell when a plane and a line are parallel to one another when given the equation of the plane? Every time this concept comes up on an exam, I blow it :x Any conceptual help would be greatly appreciated; I'll put up some questions if anyone is curious.

 

[pka]

Just remember that it is not what must students would expect.
If the direction of the line is perpendicular to the normal of the plane the two are parallel.

 

[Xibalba]

Is this because the normal vector of the plane is always perpendicular to the plane, so then for the line to be parallel to the plane it would have to be perpendicular to the vector? :?

I also want to know how I can glean the information of the line from the plane's equation?