Chapter 4, Problem 21C

Explanation of Solution

Given:

• Two lines drawn on the plane “S” are not parallel.
• Three lines do not meet at the same point on the plane “S”.

Intersection points on “S”:

• There are “$\frac{\left({\text{r}}^{\text{2}}\text{+r+2}\right)}{\text{2}}$” regions, when a single line is selected from the plane.
• The region will interact with all the lines because there are no parallel lines are drawn on the plane.
• Hence, “n” number of intersections is estimated