If the angle θ between the line x+11=y-12=z-22 and the plane 2x-y+λz+4 =0 is such that sinθ=13 . the value of λ is

Direction ratios of line are (a1, b1,c1) = (1,2,2)And direction ratios of a plane are a2,b2,c2=(2,−1,λ)∴ sin⁡θ=a1a2+b1b2+c1c2a12+b12+c12a22+b22+c22=1×2+2(−1)+2×λ12+22+2222+12+(λ)2⇒ 13=2λ35+λ⇒5+λ=4λ⇒λ=53