The state of stress in a body is uniform and is given by:

${}_{}=3$MPa;${}_{xy}=2$MPa;${}_{xz}=4$MPa

${}_{yy}=5$MPa;${}_{yz}=0$MPa;${}_{zz}=2$MPa

a$.$ Determine the principal stresses and their corresponding eigenvectors $($work must be performed by hand$)$

b$.$ Determine the stress vector on a plane oriented at $n_x=\mathrm{.}707,n_y=\mathrm{.}707,n_2=0$

c$.$ Determine the normal stress on the plane given in item $($b$)$

ALSO SHOW WORK AND STEPS ON EIGENVALUES. PLEASE