For a quadrilateral to be a parallelogram, opposite sides must be equal and parallel.
The vectors of the sides are given as:
\[
\vec{AB} = 2\hat{i} + 4\hat{j} - \hat{k}
\]
\[
\vec{BC} = -4\hat{i} + \hat{k}
\]
\[
\vec{CD} = -\hat{i} - 4\hat{j} +
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