Find the equation of the plane which passes through the points A(-1,-3,1), B(1,-2,0) and C(2,1,-1).
Calculate the shortest distance between the plane and the origin of the coordinate system.
Since A, B, and C lie in the plane, the vectors
and are parallel to the plane.
Therefore,
is normal to the plane, since it is perpendicular to .
By using the normal and the point (-1,-3,1) in the plane, we get the
point-normal form:
To find the distance between a point and a plane, use the formula: