Given vectors \(\vec{A} = 4\hat{i} - 4\hat{j} - 11\hat{k}\), \(\vec{B} = -8\hat{i} - 4\hat{j} + 4\hat{k}\), and, evaluate (a) \(\vec{A} \cdot \vec{A}\), (b) \(|\vec{A}|\), (c) \((\vec{A} \cdot \vec{B})\vec{B}\), and (d) \((\vec{B} \cdot \vec{B})\vec{A}\)\n\(\vec{A} \cdot \vec{A} = \\ |\vec{A}| = \\ (\vec{A} \cdot \vec{B})\vec{B} = (\\ \hat{i} + \\ \hat{j} + \\ \hat{k})\ (\vec{B} \cdot \vec{B})\vec{A} = (\\ \hat{i} + \\ \hat{j} + \\ \hat{k})
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