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.

Vector form:-

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.

 

Problem:-

Find the angle between the line (x+1)/ (2) =(y/3) = (z-3)/ (6)   and the plane 10x+2y-11z=3?

Answer:-

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

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