Problem $2.$ Assume the stress state at point $M$ is defined by the stress matrix $S$

$S=\left[\begin{array}{ccc}5& 1& 0\\ 1& 4& 2\\ 0& 2& 3\end{array}\right]$

A cut plane T passing through point M has direction cosines

$n_x=\frac{1}{\sqrt[\phantom{2}]{3}},n_y=\frac{1}{\sqrt[\phantom{2}]{3}},n_z=\frac{-1}{\sqrt[\phantom{2}]{3}}$

$($a$)$ Find the traction vector $t$ acting on T at point M $,$ determine its Cartesian components.

$($b$)$ Find the normal stress acting on T at point M $.$