Let \(\vec{v}=2\hat{i}+\hat{j}-\hat{k}\) and \(\vec{w}=\hat{i}+3\hat{k}\). If \(\vec{u}\) is a unit vector, then find the maximum value of \[[\vec{u} \quad \vec{v} \quad \vec{w}]\]

\([\vec{u} \quad \vec{v} \quad \vec{w}]\) denotes the Scalar Triple Product.

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