Given vectors , and
for scalars
and
:
- Plot the geometric vectors from
to
for the values
- If we let
and
run through all pairs of real numbers such that
what is the set of points
? (Just give a graphical view, no proof necessary.)
- If we consider all pairs of points
and
with
and
make a sketch of the set of points
we obtain.
- What is the set of all points
if
and
?
- What is the set of all points
if we allow
and
to be any real numbers?
- The plot is as follows (with the locus of points
for part (b) in red):
The points for each value of
are
- The set of points
as
and
run through real numbers such that
forms a line. It is drawn in red in the plot in part (a).
- The set of points in the parallelogram formed by the origin,
,
, and
.
- The horizontal band obtained by adding
to the line
for each
.
- The whole plane
.