Sheaf of Planes
A sheaf of planes with an axis, r, is a set of planes that contain the line r.
The equation of the sheaf of planes with axis, r, is:
Dividing by λ and making , the equation becomes:
Find the equation of plane that passes through the point (3, 2, −3) and belongs to the sheaf of planes with its axis on the following line:
Parallel Sheaf of Planes
Two planes are parallel if the coefficients x, y, z are proportional to their equations but their independent terms are not.
All planes that are parallel to a given plane admit an equation in the form:
Find the equation of the plane that passes through the point (3, −1, 2) and is parallel to .