|Class 12 Maths Three Dimensional Geometry||Angle between a Line and a Plane|
Angle between a Line and a Plane
The angle between a line and a plane is defined as the complement of the angle between the line and normal to the plane.
Equation of the line r->=a ⃗+λb-> and the equation of the plane r->.n->=d.
Then the angle between the line and the normal to the plane θ is given as,
The angle between line and the plane is φ= (900 – θ).
Using sin (900 – θ) =cosθ.
Find the angle between the line (x+1)/ (2) =(y/3) = (z-3)/ (6) and the plane 10x+2y-11z=3?
Let θ =angle between the line and the normal to the plane.
In Vector form: -r->= (-î+3k̂) +λ (2î+3ĵ + 6k̂)
And r->. (10 î +2 ĵ -11 k̂)=3
Here b->=2 î+3 ĵ+6 k̂ and nˆ=10 î+2ĵ-11k̂