This is a very sneaky problem!
The parametric equations of the line are: .For what value of will the line: .
intersect the plane
. . (a) in a single point . . (b) in an infinite number of points . . (c) in no points
The line has direction vector: .
The plane has normal vector: .
We find that: .
. . That is: .
Hence. the line and the plane are parallel.
In most cases, there are no points of intersection.
The sole exception is when the line lies in the plane.
. . When does this happen?
Substitute the parametric equations into the equation of the plane:
The 's cancel out and we have: .