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= (90^{0} – θ).

Using sin (90^{0} – 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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