Can 2 lines that intersect result in a plane?

Question

If I have two lines that intersect what are the possible results of intersection.

For sure the result can be a single point, or a line(line intersects with itself).

My question: Is it possible that an intersection of 2 lines can result in a plane?

Answer 1

The sets of points that make up the lines will never form an entire plane. The intersection of two lines can either be no points (unique parallel lines), one point (non parallel), or one line (if the lines are not unique).

However, two unique intersecting lines will denote a specific plane. There is only one plane that contains the two lines.

In terms of vectors. Two non-parallel vectors in $\mathbb{R^2}$ will span the plane.