Given two points representing a line and three points representing a plane, determine whether the line intersects the plane.
An obvious part of the solution is to derive, somehow, a formula for the plane, and a formula for the line.
By "a formula" we mean - this must be true - an equation, or a set of equations.
We can observe, to begin, that certain planes can be described by simple equations of the type a = b, where a is a variable and b is a constant. If b is a constant we can describe planes of the type x = b, y = b, and z = b.
However, this is not more than a starting place for a discussion of the equations that describe planes.
And, similarly, there are lines which can be described with the equations x = b, y = b, or z = b. Again, a fuller discussion is required to describe all lines.
As a final note, here, the reason we begin with planes and lines that can be described using these maximally simple equations is not only because of the simplicity of the equations, and the ease with which they can be derived and understood, but also because some planes of this type cannot be described using the normal equations that more generally describe planes and lines.
For a similar reason we are beginning this discussion by determining whether a line and a plane intersect, or do not intersect. This is an initial step, and our larger purpose, for the moment, is to calculate the location of a point at which a line and a plane intersect ... if they do intersect.
