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
is the unique point in