Some common vocabulary:

A set of points and/or lines is said to be "coplanar" if
there is a single plane containing them all.

Lines in R^2 are said to be parallel if they don't meet.  We discussed
how this is consistent with high school geometry.  Watch out, this
definition will have to change when we discuss the extended plane E^2
or three-dimensional space R^3.

Definitions we agreed on in class, for now:

We decided that in R^3 there are two definitions of "parallel" for lines.

1. Lines are parallel if they are coplanar but either don't meet 
or are the same line.

2. Lines are parallel if they have the same slope vector.

Note that the second definition implies that, for lines in R^3,
being parallel is an equivalence relation.  This is one reason
we choose to consider a line to be parallel to itself.

We believe (but didn't prove) that these are equivalent definitions:
one is true if and only if the other is true.  We are not going
to prove they are equivalent because that takes us into coordinate
geometry and slope vectors, which we don't plan to delve into in this course.

OPTIONAL EXERCISES:

If you know what a slope vector is, you can probably prove that
(2) implies (1).  Try it if you want.

Can you argue that (1) implies (2)?  I think this is harder.

If you have anything to say about either of these, Monday or Wednesday,
please let me know at the beginning of class Monday or Wednesday and
we'll fit in a discussion and see where it goes.

PLANES:

Two planes are said to be parallel if they don't meet or are the same plane.

A line and a plane are said to be parallel if they don't meet or
the line is contained in the plane.