$4\mathrm{.}4[$SEcTIION $4\mathrm{.}2]$ The rectangular Cartesian components of a particular Cauchy stress tensor are given by

Determine the unit normal $n$ of a plane parallel to the $x_3$ axis $($i$.$e$.n_3=0)$ on which the traction vector is tangential to the plane. What are the constraints on a and $b$ necessary to ensure a solution?

If $a,b,c,d$ and $e$ are functions of $x_1$ and $x_2,$ find the most general forms for these functions that satisfy stress equilibrium in Eqn. $(4\mathrm{.}27)$ in the absence of body forces.