Two points on the line (L say )3x=2y,z=1 are
(0,0,1)&(3,2,1)
So dr's of the line is <3,2,0>
Line passing through (1,2,1), parallel to L and
coplanar with given plane is r=i^+2j^+k^+t(3i^+2j),t∈R(−2,0,1) satisfies
the line ( for t=−1) ⇒(−2,0,1) lies on given plane.
Answer of the question is (2)
We can check other options by finding equation of plane
Equation plane : ∣∣x−11+22+2y−22−01−0z−11−12−1∣∣=0 ⇒2(x−1)−3(y−2)−5(z−1)=0 ⇒2x−3y−5z+9=0