1. Pick a point ON the line, (f0,1,2) for example, and set up the equation governing this.
You have three unknowns (essentially, the components of the normal vector).
Utilize the fact that irrespective of the value of t, the whole line should be included in the plane.
This will give you a single equation for the three unknowns.
2. Also require that the given solitary point should lie in the plane.
This will give you the second equation for your three unknowns.
This is what you need, you'll end up with a free scaling parameter for the normal (i.e, its length), as you should.