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Math 1220 Instructor: Mike Shrieve Practice Midterm #1 Name: The midterm is 50 minutes. No calculators or equation sheets are allowed. Answer all questions. (1) Let ~u = h4, 2, −7i and ~v = h−1, 3, 6i. Calculate the following: (a) ~u + ~v (b) ~u · ~v (c) ~u × ~v (d) Proj~v ~u (2) Write an equation for the plane passing through the points (1, 4, 5), (−2, 6, −1), and (0, 0, 0). (3) Write an equation for the plane passing through the origin which is orthogonal to both the plane x + y + z = 7 and the plane 4x − 2y = 1. (4) Write a parametric equation for the tangent line to the curve given by the vector function ~r(t) = ht2 , 7t, 4t − 1i at t = 4.