We know that equation of plane passing through the line of intersection of the planes is
→r.(→a+λ→b)=c1+λc2
where →a and →b are the normal vectors of the planes and c1 and c2 are the intercept terms of the respective planes.
So, here, equation of the required plane is,
→r.((2+λ)^i+(−3+5λ)^j+(1−λ)^k)=3+4.4λ
It is given that (2,−1,1) passes through the plane.
⟹(2^i−^j+^k).((2+λ)^i+(−3+5λ)^j+(1−λ)^k)=3+4.4λ
⟹2(2+λ)−(−3+5λ)+(1−λ)=3+4.4λ
4+2λ+3−5λ+1−λ=3+4.4λ
8.4λ=5
Substituting λ=5/8.4 we get the equation as,
→r.((21.8)^i+(−0.2)^j+(3.4)^k)=47.2