Geometria Analítica: Ângulo entre Dois Planos

Abstract

**Video Summary — Angle Between Two Planes**

The video uses a **three-dimensional perspective and geometric animations** to explain the concept of the angle between two intersecting planes.

Through the rotation of the planes, it illustrates the relationship between the angle formed by the planes and the angle between their normal vectors.

The video also examines the case in which the angle between the normal vectors is obtuse, showing why its supplementary angle is considered.

An algebraic derivation justifies the use of the absolute value in the formula for the cosine of the angle between two planes:

**cos θ = |n⃗₁ · n⃗₂| / (‖n⃗₁‖ ‖n⃗₂‖)**

where θ is the angle between the normal vectors n⃗₁ and n⃗₂ of the planes.

This approach combines **three-dimensional visualization, geometric interpretation, and algebraic reasoning**, facilitating a deeper understanding of the concept.