(b) Show that u, v, and w are coplanar, using the definition that there exist two nonzero real numbers a and ẞ such that w = au + ẞv. Consider the plane formed by u and v in standard position. Then au + ẞv, is the vector that represents the diagonal of the parallelogram formed by au and ẞv. If nonzero real numbers α and ẞ exist such that w = au + ẞv, then u, v, and w coplanar. So we must show nonzero real numbers & and ß | exist such that w = au + ẞv. Thus, equating components in (0, -9, 18) a(1, 4, −7)+ ß(2, −1, 4), we want to solve the following system. = = a + 2ẞ 4a β = -7α + 4ẞ The solution to this system is (a, ẞ) v, and w (If an answer does not exist, enter DNE.) Thus, nonzero real numbers α and ẞ exist such that w = au + ẞv, so vectors u, coplanar.