Theorems · Theorem · geometry

Orientation.inner_smul_rotation_pi_div_two_smul_left

∀ {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 : V) (r₁ r₂ : ℝ), inner ℝ (r₁ • (o.rotation ↑(Real.pi / 2)) x) (r₂ • x) = 0

The inner product between a multiple of a π / 2 rotation of a vector and a multiple of that vector is zero.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

2 results in Mathlib

Foundations

Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact