Consider a triangle \(\triangle OAB.\) If \(\overrightarrow{OA}=(0,2,-2)\) and \(\overrightarrow{OB}=(1,-4,1),\) then what is the area of \(\triangle OAB?\)

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Calculate the area of the triangle spanned by the vectors \( \vec{a}\) and \( \vec{b}, \) where \( \lvert \vec{a} \rvert = 3 ,\) \( \lvert \vec{b} \rvert = 4 \) and \( \vec{a} \cdot \vec{b} = 8\sqrt{2}.\)

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