Families of planes

The family of planes containig a straight line r

is:

or:

The family of parallel planes to a plane π

is

 

 

Exercises:

1.- Find the plane that is parallel to x - 3y + z - 8 = 0 and passes through the origin.

 

2.- Find the plane that contains the straight line r and passes through the point (3,3,3), where:

 

Solutions: 1) x - 3y + z = 0; 2) 8x + 3y - 10z - 3 = 0