Vectors, line contained within plane

[craka]

Homework Statement

It seems to be obvious. But would like to check that for a line to be contained in a plane it needs to be parallel. Correct?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

parallel to what?

Parallel to the plane? No, a line that is contained in the plane is not, by definition, "parallel" to that plane. In order to be parallel, the line must have no points in common with the plane which is clearly not true if it is contained in the plane.

It is true that if a line is contained in a plane then its direction vector is perpendicular to the normal vector of the plane.