4. Intersections of Lines & Planes In three-space, there are three possibilities for the intersection of a line and a plane: S prev by (a) They intersect at a point. (b ) They are coincident / coplanar ( C ) They are parallel and distinct Given the line h: [x, y, z] = [2, 3, -1] + t [4, 1, 2] Give an example of an equation of a plane for each possible intersection Prove / Justify your results for each. (You can use algebra or geometric proofs to show that you have a valid example.) The equations of the line and planes are clearly stated and indeed represent 16T the examples they were chosen for (3 x 2 marks for each type) Clarity for your proofs / justifications /4T (intersect at a point, 2 marks, all others, 1 mark)