1. If Yoda says to Luke Skywalker, "The Force be with you," then the dot product of the Force and Luke should be: (a) negative (b) zero (c) positive (d) any real number Explain your answer. 2. Some warm-up problems: (a) Show that the angle between (6, 3, -2) and (4, 2, 4) is arccos 2. (b) Find the projection of u = (3, 3, 4) onto v = (1,4, -1). (c) Determine which of the following are orthogonal to each other: (2, 3, 10), (4, 2, -1) and (2, 3, 14). (d) Given (1, 2, -4), find a vector that is orthogonal to it. Can you find infinitely many such vectors? What geometric object do these vectors form in 2-dimensions and 3-dimensions