(a) Does the plane $\vec r(s,t) = \left(5s-3\right)\,\mathit{\vec i}+\left(1-t\right)\,\mathit{\vec j}+\left(2s+2t\right)\,\mathit{\vec k}$ contain the point $\left(-13,3,-8\right)$? ? yes no

(b) Find the $z$-component of the point $(-8, -1, z_0)$ so that it lies on the plane.
$z_0 =$
For what values of $s$ and $t$ is this the case?
$s =$
$t =$