Let be the plane determined by the three points , , and . Find the following:
- A normal vector to the plane.
- A Cartesian equation for the plane.
- The distance between the plane and the origin.
- Denote the points by , and , then we can compute a normal vector by
Therefore, is a normal vector to the plane.
- Since is normal to the plane we have a Cartesian equation of the form
Then, since is on the plane we have . Hence, the Cartesian equation is
- The distance from the origin is