Answer
(a) $t=1$
(b) $(3,3,4)$
Work Step by Step
(a) Plug-in the parametric $x, y, z$ line equations into the plane equation, we get $5(2+t)-2(3t)-2(5-t)=1$ which leads to $10+5t-6t-10+2t=1$ and thus we have $t=1$
(b) The intersection point can be found by plug-in $t=1$ into the equations, we get $x=3, y=3, z=4$ or point $(3,3,4)$
