Linear Transformations · Superchallenge problem

A linear map $T:\mathbb{R}^3\to\mathbb{R}^3$ satisfies $T(\mathbf v)\cdot\mathbf v = 0$ for every vector $\mathbf v$. Moreover $T(1,2,2) = \mathbf 0$ and $T(1,0,0) = (0, 2, -2)$. Find the $x$-coordinate of $T(0,1,0)$.