# Angle Between Line and a Plane

#### 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|)|

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