The magnitude of the resultant of two vectors lies between the range of their sum and the difference. For vectors of magnitudes 4 units and 8 units, the possible resultant must be between:
\(\ \ |8 - 4| = 4 \text{units} \quad \text{and} \quad 8 + 4 = 12 \text{units}.\)
Let $ \vec{a} = \hat{i} + 2\hat{j} + \hat{k} $, $ \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k} $, $ \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k} $ and $ \vec{d} $ be a vector such that $ \vec{b} \times \vec{d} = \vec{c} \times \vec{d} $ and $ \vec{a} \cdot \vec{d} = 4 $. Then $ |\vec{a} \times \vec{d}|^2 $ is equal to _______
Match List-I with List-II and select the correct option: 