= Solution
The vector $(0,1,-1)$ is an <eigenvector> with <eigenvalue> one. The other two orthogonal directions give eigenvalues two and five, leading to
$$
\boxed{V=\begin{pmatrix}
0&1/\sqrt3&2/\sqrt6\\
1/\sqrt2&1/\sqrt3&-1/\sqrt6\\
-1/\sqrt2&1/\sqrt3&-1/\sqrt6
\end{pmatrix},\qquad D=\operatorname{diag}(1,2,5).}
$$
Its columns are an <orthonormal eigenbasis>, so $V^{\mathsf T}V=I$ and $V^{\mathsf T}AV=D$. Multiplying by $V$ and $V^{\mathsf T}$ gives $\boxed{A=VDV^{\mathsf T}}$. Eigenvector signs and the joint order of columns and diagonal entries may be changed consistently.
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