Given the parallelepiped
I need to find the equation of the line through the points $A$ and $F$. I know the line which contains $DG$ has equation given by
$$X=t(1,2,-3),\quad t\in\mathbb{R}$$
and $F(0,2,0)$. My question is: may I say the equation I need to find is given by
$$X=(0,2,0)+\lambda(1,2,-3),\quad\lambda\in\mathbb{R}$$ since the vectors $AF$ and $DG$ are parallels?