A parallelogram is placed in 3D space with one of its vertices at the origin, O (0, 0, 0). The second vertex is at point P(4, 2, 4) with vector $\overrightarrow{OP} = \vec{p}$. The third vertex is at point Q(3, 1, 4) with vector $\overrightarrow{OQ} = \vec{q}$. The last vertex is at point R with unknown coordinates. A line is drawn from point Q perpendicular to side PR of the parallelogram to intersect PR at point S. Using vectors determine the length of QS. A picture will be helpful and recall the formulas for the area of a triangle ($A = \frac{b \times h}{2}$) and parallelogram ($A = b \times h$). [T:/6]
