Explanation:
Parallel (geometry)
Parallelism is a
term in geometry and in everyday life that refers to a property in Euclidean
space of two or more lines or planes, or a combination of these. The existence and properties of parallel
lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not intersect or
meet are called parallel lines.
http://en.wikipedia.org/wiki/Parallel_(geometry)
Line (geometry)
The notion of line or straight line was introduced by the ancient
mathematicians to represent straight objects with negligible width and depth. Lines are an idealization
of such objects. Thus, until seventeenth century, lines were defined like this:
"The line is the first species of quantity, which has only one dimension,
namely length, without any width nor depth, and is nothing else than the flow
or run of the point which [...] will leave from its imaginary moving some
vestige in length, exempt of any width. [...] The straight line is that which
is equally extended between its points"
A line segment is a part of a line that is
bounded by two distinct end points and contains every point on the line between
its end points. Depending on how the line segment is defined, either of the two
end points may or may not be part of the line segment. Two or more line
segments may have some of the same relationships as lines, such as being
parallel, intersecting, or skew.
Vector equation
The vector equation of the line through points A and B is given
by r = OA + λ AB (where λ is a scalar multiple)
If a is vector OA and b is vector OB, then the equation of
the line can be written: r = a + λ (b - a)
A ray starting at point A is described by limiting
λ≥0
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Line_(geometry)
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution-
ShareAlike 3.0 Unported License.