Theorems · Theorem · geometry

Orientation.inner_eq_norm_mul_norm_mul_cos_oangle

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) (x y : V), inner ℝ x y = ‖x‖ * ‖y‖ * (o.oangle x y).cos

The inner product of two vectors is the product of the norms and the cosine of the oriented angle between the vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

1 results in Mathlib

Foundations

Depth 277 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact