$($a$)$ Find a vector$-$parametric equation vec$(r{)}_1(t)=($:$x(t),y(t),z(t)$:$)$ for the shadow of the circular cylinder $x^2{z}^2=4$ in the $xz-$plane.

Shadow: vec$(r{)}_1(t)=,$ for $0t2.$

$($b$)$ Find a vector$-$parametric equation for intersection of the circular cylinder $x^2{z}^2=4$ and the plane $7x6y3z=1.$

Intersection: vec$(r{)}_2(t)=,$ for $0t2.$