Consider in $\mathbb{R}^3$ two reference systems $S = (O; \vec{e}_1, \vec{e}_2, \vec{e}_3)$ and $S' = (O'; \vec{e}'_1, \vec{e}'_2, \vec{e}'_3)$ with $OO' = (-2, 3, 9)$ in $S$, $\vec{e}'_1 = \vec{e}_1 + 3\vec{e}_2 + \vec{e}_3$, $\vec{e}'_2 = -\vec{e}_1$ and $\vec{e}'_3 = 2\vec{e}_1 + 5\vec{e}_2 + 7\vec{e}_3$. Find the equation in $S'$ of the plane whose equation is $2x -3y + z = 2$.
I have no idea how to go about this except for the steps in this picture.
