Directions: Answer the questions below. Make sure to justify your responses. A. [10 pts] Suppose that' u = (3, a, 1) and v = (2, 4,3). Find all values of real values of a so scal - u = scale v or explain why there are no such real a-values. Q Edit & Create B. [10 pts] Suppose that u and v are nonzero vectors in R3. A well-known fact is that if u and v are parallel, then u x v = 0. i. [5 pts] Recall that Ju x v| = u v sin(0), where 0 is the interior angle between u and v. Use this formula to explain why u x v = 0 if u and v are parallel. ii. [5 pts] Suppose that u = (11, 12, us). Recall that two nonzero vectors u and v are parallel if and only if there is a scalar c so u = ev. Use this fact to exhibit the components of v in terms of the components of u, then compute u x v. dd to 8% Edit & Create C. [10 pts] Suppose that u, v, and w are three nonzero vectors in the ryz-plane. Morgan claims that if u . w = v . w, then u = v. Explain whether Morgan's argument is correct or incorrect. If the argument is incorrect, then find three nonzero vectors u, v, and w such that u . w = vow but u / v