Let be the line through the point
and parallel to the vector
and let
be a point not on
. Find a Cartesian equation for the plane
which passes through
and entirely contains
.
The line is the set of points
Then, the plane is the set of points
Then, to get the Cartesian equation, we have
The first two equations give and so
. This implies
, and
is arbitrary. So, the plane is described by the equation
.