Hello, Sam!

This is a verysneakyproblem!

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 arepoints of intersection.no

The sole exception is when the line liesthe plane.in

. . When does this happen?

Substitute the parametric equations into the equation of the plane:

. .

The 's cancel out and we have: .

Therefore: .