Coordinates in an Orthogonal Basis

The set $\{\mathbf{u}_1, \mathbf{u}_2, \mathbf{u}_3\}$ below is an orthogonal basis of $\mathbb{R}^3$ (every pair has dot product zero — you can verify this quickly):

$\mathbf{u}_1 = (2,\ 1,\ 2), \qquad \mathbf{u}_2 = (1,\ 2,\ -2), \qquad \mathbf{u}_3 = (-2,\ 2,\ 1)$

Note that it is orthogonal, not orthonormal. Write the vector $\mathbf{x} = (6,\ 3,\ -3)$ in this basis as

$\mathbf{x} = c_1\mathbf{u}_1 + c_2\mathbf{u}_2 + c_3\mathbf{u}_3$

What is $(c_1,\ c_2,\ c_3)$?