Q. 135.0( 2 Votes )

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

Answer :

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.


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