The position vectors of points A, B, C and D are \(\mathbf{A} = 3\hat{i} + 4\hat{j} + 5\hat{k}, \mathbf{B} = 4\hat{i} + 5\hat{j} + 6\hat{k}, \mathbf{C} = 7\hat{i} + 9\hat{j} + 3\hat{k}\) and \(\mathbf{D} = 4\hat{i} + 6\hat{j}\) then the displacement vectors AB and CD are
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\vec{AB} = (4\hat{i} + 5\hat{j} + 6\hat{k}) - (3\hat{i} + 4\hat{j} + 5\hat{k}) = \hat{i} + \hat{j} + \hat{k}
\overrightarrow{CD} = (4\hat{i} + 6\hat{j}) - (7\hat{i} + 9\hat{j} + 3\hat{k}) = -3\hat{i} - 3\hat{j} - 3\hat{k}
\overrightarrow{AB} and \overrightarrow{CD} are parallel, because its cross-products is 0.
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