$4\mathrm{.}18**$ Use the property $(4\mathrm{.}35)$ of the gradient to prove the following important results: $($a$)$ The vector Vf at any point r is perpendicular to the surface of constant f through r$.($Choose a small displacement dr that lies in a surface of constant f$.$ What is df for such a displacement?$)($b$)$ The direction of Vf at any point r is the direction in which f increases fastest as we move away from r$.($Choose a small displacement dr $=$ u$,$ where u is a unit vector and & is fixed and small. Find the direction of u for which the corresponding df is maximum, bearing in mind that a b $=$ ab cos O$.)$