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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