1. The problem statement, all variables and given/known data Let us consider three scalar fields u(x), v(x), and w(x). Show that they have a relationship such that f(u, v, w) = 0 if and only if (∇u) × (∇v) · (∇w) = 0. 2. Relevant equations 3. The attempt at a solution I could think nothing but just writing the components of (∇u) × (∇v) · (∇w) = 0. How could i prove this?