Given a line and a point not on the line, how many line segments can be drawn that connect the point to the line so that the segment and the line are perpendicular in 2-space? In 3-space?
In 2-space, it would have to be a 1 unique line segment. Is it the same in 3-space?
Note that any line segment that goes through a line and a point not on the line, must be in the plane defined by the line and the point. Hence, we can reduce the problem down to 2 dimensions in that plane, in which case the aforementioned theorem holds.