Consider the quadrilateral (four-sided plane figure) formed by the points P(3,3, 2), Q(3, 4, 3), R(8,8, 3), and S(8,7, 2), in this order. (a) Show that the quadrilateral is actually a parallelogram, i.e. opposite sides of the quadrilateral are parallel. [Hint: create vectors from the sides PQ, QR, RS, SP of the quadrilateral and use Theorem 12 in the notes: two vectors u and v are parallel precisely when u = cv for some scalar c) (b) Find the area of this parallelogram using the cross-product area formula in the notes.

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