If angle θ between the line  x+11=y−12=z−22 and the plane 2x−y+λz+4=0 is such that  sin⁡θ=13,the value of λ is

The line is x+11=y−12=z−22 and the plane is  2x−y+λz+4=0If θ is the angle between the line and the plane, then 90o - θ is the angle between the line and normal to the plane. Thus, cos⁡90∘−θ=(1)(2)+(2)(−1)+(2)(λ)1+4+44+1+λor  sin⁡θ=2−2+2λ35+λ or 13=2λ35+λor  5+λ=2λor  5+λ=4λor  3λ=5or  λ=53