Show that [∂r/∂u1, ∂r/∂u2, ∂r/∂u3] = h1 h2 h3 = 1/[∇u1, ∇u2, ∇u3].

Question

Show that vector [∂r/∂u₁, ∂r/∂u₂, ∂r/∂u₃] = h₁ h₂ h₃ = 1/[∇u₁, ∇u₂, ∇u₃].

Answer 1

By definition of unit vectors,