Show that the normal to the following pairs of planes are perpendicular to each other:
i. x – y + z – 2 =0 and 3x + 2y – z +4=0
ii. and
i. The vector equation of the plane x-y+z-2=0 can be written as
The normal to this plane is
The vector equation of the plane 3x + 2y – z +4=0 can be written as
The normal to this plane is
Now
Hence is perpendicular to
Therefore, the normal to the given pairs of planes are perpendicular to each other.
ii. The equation of the first plane is
The normal to this plane is
The equation of the first plane is
The normal to this plane is
Now
Hence is perpendicular to
Therefore, the normal to the given pairs of planes are perpendicular to each other.