Answer
$(\dfrac{3}{2},\dfrac{-3}{2},\dfrac{1}{2})$
Work Step by Step
Since, we have the parametric equations $x=1-t; y=3t; z=1+t$
Equation of plane $2x-y+3z=6$
Plug all the parametric equations $x=1-t; y=3t; z=1+t$
in the equation of plane, we have $t=\dfrac{-1}{2}$
Thus, we have the Parametric equations as follows: $x=1-(\dfrac{-1}{2})=\dfrac{3}{2}; y=3(\dfrac{-1}{2})=\dfrac{-3}{2}; z=1+(\dfrac{-1}{2})=\dfrac{1}{2}$
Hence, the line will meet at the point: $(\dfrac{3}{2},\dfrac{-3}{2},\dfrac{1}{2})$
