Given a line and a point not on the line, determine the following. How many line segments can be drawn that connect the point to the line in 2- space? In 3-space?
In 2-space I think it would be infinite number of lines. What do you think? I sit the same for 3-space too?
Yes, you're right. There are infinitely (in fact uncountably) many points on the line, and each, together with the point not on the line, determines a different line segment, whether in two or in three dimensions.