#### definition

The angle between a line and a plane is the complement of the angle between the line and normal to the plane Fig.

#### notes

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

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#### Shaalaa.com | 3 Dimensional Geometry part 27 (Angle between line and plane)

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