Coordinates with respect to an orthonormal basis

Verify that the vectors

$$e_1=\frac{1}{3}(1,2,2),e_2=\frac{1}{3}(2,1,-2),e_3=\frac{1}{3}(2,-2,1)$$

form an orthonormal basis of ${\mathbb{R}}^3$ and compute the coordinates of $v=(3,3,3)$ with respect to this basis.