9709 P32 - Jun 2016 - Q9I - 5 marks
2152
The points A, B and C have position vectors, relative to the origin O, given by \(\overrightarrow{OA} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k}\), \(\overrightarrow{OB} = 4\mathbf{j} + \mathbf{k}\) and \(\overrightarrow{OC} = 2\mathbf{i} + 5\mathbf{j} - \mathbf{k}\). A fourth point D is such that the quadrilateral ABCD is a parallelogram.
Find the position vector of D and verify that the parallelogram is a rhombus.
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