Position vector of D is
$$\mathbf{d} = \mathbf{c} + \overrightarrow{CD}$$
But AB and CD are on opposite sides of the rectangle, therefore:
$$\overrightarrow{AB} = \overrightarrow{CD}$$
So,
$$\mathbf{d} = \mathbf{c} + \overrightarrow{AB} = \mathbf{c} + (\mathbf{b} - \mathbf{a})$$
Plugging in the numbers:
$$\mathbf{d} = \mathbf{c} + (\mathbf{b} - \mathbf{a})$$
$$= (4, 5, -1) + ((2, -1, 0) - (1, 2, 2))$$
$$= (4, 5, -1) + (1, -3, -2)$$
$$= (5, 2, -3)$$


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