What is the distance between two points in space?
We define the distance between two points in
space as the length of the line segment
connecting them.
In terms of their coordinates $(x_1, x_2, x_3),
(y_1, y_2, x_3) \in \R ^3$, the
space distance of two
points is
\[
\sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + (x_3 - y_3)^2}.
\]