Problem $1(33$ points$)$: Strain field within a loaded continuum

Given the strain tensor, at a given point $M,{}_{{?}_{?}}(M)=([a,0,b],[0,c,0],[b,0,d]{)}_{(vec(e{)}_1,\text{v}\text{e}\text{c}(e{)}_2,\text{v}\text{e}\text{c}(e{)}_3)}$MPa with $a=8,b=3,c=6,$ and $d=10$

Determine the elongation in the direction vec$(n)=9$vec$(e{)}_1+5$vec$(e{)}_2+8$vec$(e{)}_3$

Determine the direction the highest elongation and the magnitude of this elongation