Relative to a fixed origin OOO, the point A A\,A has position vector (2i−3j+4k)(2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k})(2i−3j+4k), the point B B\,B has position vector (5i−10j+2k)(5\mathbf{i} - 10\mathbf{j} + 2\mathbf{k})(5i−10j+2k), and the point C C\,C has position vector (3i−7j−2k)(3\mathbf{i} - 7\mathbf{j} - 2\mathbf{k})(3i−7j−2k).
Find BC⃗\vec{BC}BC
Show that the quadrilateral OABC OABC\,OABC is a parallelogram, giving reasons for your answer.
