Let Equation of plane passing through (2,1,3) is l(x−2)+m(y−1)+n(z−3)=0 ...(i) This plane is perpendicular to x−2y+2z+3=0 and 3x−2y+4z−4=0 ⇒l−2m+2n=0 and 3l−2m+4n=0 ⇒
l
−8+4
=
m
6−4
=
n
−2+6
⇒
l
−4
=
m
2
=
n
4
⇒
l
−2
=
m
1
=
n
2
From Eq. (i), ∴−2(x−2)+(y−1)−2(z−3)=0 ⇒−2x+4+y−1+2z−6=0 ⇒−2x+y+2z−3=0 ⇒2x−y−2z+3=0