Let \( \vec{u} = \hat{i} - \hat{j} - 2\hat{k} \), \( \vec{v} = 2\hat{i} + \hat{j} - \hat{k} \), \( \vec{v} \cdot \vec{w} = 2 \) and \( \vec{v} \times \vec{w} = \vec{u} + \lambda \vec{v} \). Then \( \vec{u} \cdot \vec{w} \) is equal to:
\( \dfrac{3}{2} \)
\( 2 \)
\( 1 \)
\( -\dfrac{2}{3} \)
