KEAM 2012 Math Paper

Let the equation of plane parallel between 2x−2y+z+3=0
and ‌‌2x−2y+z+‌

9

2

=0 is
2x−2y+z+c=0
Now, distance between two given parallel lines
=‌

‌ 9 2 −3

√22+22+12

=‌

3/2

3

=‌

1

2

∵ Required plane is equidistant from given planes
∴‌‌‌

c−3

√22+22+12

=‌

1∕2

2

⇒‌‌‌

c−3

3

=‌

1

4

⇒‌‌c=‌

3

4

+3
⇒‌‌c=‌

15

4

∴ Required equation of plane is
∴‌‌2x−2y+z+‌

15

4

=0
⇒‌‌8x−8y+4z+15=0