The angle between a line and a plane is the complement of the angle between the line and normal to the plane Fig.
Vector form If the equation of the line is `vec r = vec a + lambda vec b` and the equation of the plane is `vec r . vec n = d .` Then the angle θ between the line and the normal to the plane is
cos θ = `|(vec b . vec n)/(|vec b| . |vec n|)|`
and so the angle φ between the line and the plane is given by 90 – θ, i.e.,
sin (90 – θ) = cos θ
i.e. sin φ = `|(vec b . vec n)/(|vec b| . |vec n|)|` or
φ =`sin ^ (–1)` `|(bar b . bar n)/(|bar b| . |bar n|)|`
Video link : https://youtu.be/9BKeK0D9unc