Let $H(u, v)=a u^2+b u v+c v^2$ be a quadratic function. (a) Prove that the nonequilibrium trajectories of the associated Hamiltonian system and those of the gradient flow are mutually orthogonal, i.e., they always intersect at right angles. (b) Verify this result for the particular quadratic functions (i) $u^2+3 v^2$, (ii) $u v$, by drawing representative trajectories of both systems on the same graph.