If the angle θ between the line  and the plane 2x - y + √λ z + 4 = 0 is such that sin . The value of λ is-

Concept:

If the equation of a line is  and the equation of the plane is  

Then the angle between line and plane can be obtained by:

, Where  are d.r's of line and normal to the plane.

Calculation:

Given:

Direction ratio of line = (1, 2, 2)

Equation of plane is  2x - y + √λ z + 4 = 0 

Direction ratio of normal to the plane = (2, -1, √λ)

sin 

Now,

Squaring both sides, we get