Question

Describe the possible configurations and the possible number of points of intersection of (a) 2 lines in the plane (b) 3 lines in the plane (c) 2 lines in space (d) 3 planes in space.

Answer 1

Answer:  The answer is given below.

Step-by-step explanation: The description is as follows:

(a) 2 lines in the plane : Any two lines in a plane can either be parallel or intersect at only one point.

(b) 3 lines in the plane : Any three lines in a plane may intersect at a point, if so, they are called concurrent lines, or they may never intersect.

(c) 2 lines in space :  There are exactly three possibilities.

* The two lines are distinct and they have no points in common.

* The two lines are distinct and they have exactly one point in common.

* The two lines are really the same line and they have all of their points in common.

(d) ) 3 planes in space : Here also, we have three possibilities:

* The three planes are distinct and they have no points in common.

* The three planes share exactly one point.

* The three planes share infinitely many points, i.e., they could all share a line or they could all be the same plane.