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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