Relative to a fixed origin OOO, the point P P\,P has position vector (3i+5j−k)(3\mathbf{i} + 5\mathbf{j} - \mathbf{k})(3i+5j−k), the point Q Q\,Q has position vector (4i+3j+2k)(4\mathbf{i} + 3\mathbf{j} + 2\mathbf{k})(4i+3j+2k), and the point R R\,R has position vector (3i−6j+9k)(3\mathbf{i} - 6\mathbf{j} + 9\mathbf{k})(3i−6j+9k).
Find PQ⃗\vec{PQ}PQ
Show that the quadrilateral OPQR OPQR\,OPQR is a trapezium, giving reasons for your answer.
