Question

Do two intersecting lines ALWAYS determine a plane?

Answer 1

In theory, yes.

Explanation:

"If two lines intersect, then exactly one plane contains the lines." Now, each line contains two points, and according to another theorem in my book: "If two lines intersect, then they intersect in exactly one point." and three noncollinear points define a plane.

Answer 2

Answer: Yes.

Explanation:

Two intersecting lines determine a plane. If you hold two pencils so that they cross each other, there’s only one place a flat plane can be placed so that it rests on both pencils. Which lines are always co planar? Two lines in three-dimensional space are coplanar if there is a plane that includes them both.