Theorems · Theorem · linear algebra
InnerProductGeometry.norm_ofLp_crossProduct
∀ (a b : EuclideanSpace ℝ (Fin 3)), ‖WithLp.toLp 2 ((crossProduct a.ofLp) b.ofLp)‖ = ‖a‖ * ‖b‖ * Real.sin (InnerProductGeometry.angle a b)
The L2 norm of the cross product of two real vectors (of type EuclideanSpace ℝ (Fin 3))
equals the product of their individual norms times the sine of the angle between them.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
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- SeminormedAddCommGroupproof · cited by 2,671
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Inner.innerproof · cited by 1,089
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductGeometry.norm_toLp_symm_crossProductproof · cited by 0