Consider the line through the point
and parallel to the vector
. Then, let
be the plane through the point
and spanned by the vectors
and
. Prove that there is exactly one point in
, and determine the point.
Proof. First, we have that and
are the sets of points
Then, the points in
are those which satisfy
This gives us the Cartesian equation
The points on
are those such that
Thus, if then we have
Hence,
is the unique point in