Angle Between Two PlanesAngle Between Two Planes - Planes & Angles - Practice Questions & MCQ

The angle between two planes is defined as the angle between their normals.

Let Ө be the angle between two planes and  then,

Condition for Perpendicularity of Two Plane

If the planes and are perpendicular, then and are perpendicular.

Therefore .

Condition for Parallelism of Two Plane

If the planes and are parallel, then there exists a scalar λ such that  .

Cartesian Form

Let θ be the angle between the planes, a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0 .

Then,

The direction ratios of the normal to the planes are a₁, b₁, c₁  and a₂, b₂ c₂ respectively.
 

Condition for Perpendicularity of Two Planes

If the planes are at right angles, then θ = 90^o and so cos θ = 0. Hence, cos θ = a₁a₂ + b₁b₂ + c₁c₂ = 0.
 

Condition for Parallelism of Two Plane

If the planes are parallel, then