Linear Transformations · Hard problem

Let $T:\mathbb{R}^3\to\mathbb{R}^3$ be the (oblique) projection onto the plane $x + y + z = 0$ along the direction $\mathbf d = (1,2,3)$: each point $\mathbf v$ is moved parallel to $\mathbf d$ until it lands on the plane. Find the $y$-coordinate of $T(2,5,5)$.