HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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Angle Between Line and a Plane

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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

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

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3 Dimensional Geometry part 27 (Angle between line and plane) [00:06:14]
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