In each of the following cases determine if the given set of points all lie on the same line.
-
,
,
.
-
,
,
.
-
,
,
.
- The points
are not on the same line since the unique line containing
is given by
But,
cannot be on this line since for any
, the third coordinate of every point on the line will be 1, while the third coordinate of
is
.
- The points
are not on the same line since the unique line containing the points
is given by
But,
is not on this line since if
then we must have
. However, with
we have
.
- The points
are not on the same line since the unique line containing the points
is given by
But then
is not on this line since if
then
, but then
. Hence,
is not on the line.