Singular Values & the SVD · Hard problem

Among all solutions of the single equation $x + 2y + 2z = 9$, the pseudoinverse picks the one of smallest length, $\mathbf{x}^{+} = A^{+}b$ with $A = \begin{pmatrix}1 & 2 & 2\end{pmatrix}$, $b = 9$. Find $\|\mathbf{x}^{+}\|$.