The equation of the required plane is given as, a(x−2)+b(y+1)+c(z−3)=0 …… (1) since, the plane is perpendicular to 3x−2y+z=9 then, 3a−2b+c=0 …… (2) The required plane is also perpendicular to x+y+z=9 ,a+b+c=0 …… (3) From equation ( 2 ) and equation ( 3 ),
a
−2−1
=
b
1−3
=
c
3+2
Assume,
a
−3
=
b
−2
=
c
5
=λ The equation (1) can be written as, −3λ(x−2)−2λ(y+1)+5λ(z−3)=0 x+