$1\mathrm{.}70.$ The stress at a point in a machine component relative to an $x,y,z$ coordinate system is

given by

$\left[\begin{array}{ccc}100& 40& 0\\ 40& 60& 80\\ 0& 80& 20\end{array}\right]$MPa

Referring to the parallelepiped shown in Fig. P$1\mathrm{.}70,$ calculate the normal stress $$ and the shear

stress $$ at point $Q$ for the surface parallel to the following planes: $($a$)$ CEBG, $($b$)$ ABEF, $($c$)$

AEG. $[$Hint: The position vectors of points $G,E,$A and any point on plane AEG are,

respectively, $r_g=3i,r_e=4j,r_a=2k,r=+yj+zk.$ The equation of the plane is given by

$(r-r_g)*(r_e-r_g)(r_a-r_g)=0$