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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 200 7 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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18.02 Practice Exam 1 A Problem 1. (15 points) A unit cube lies in the first octant, with a vertex at the origin (see figure). −−� −−� a) Express the vectors OQ (a diagonal of the cube) and OR (joining O to the center of a face) in terms of ˆ ı, ˆ k. �, ˆ O Q R z y x b) Find the cosine of the angle between OQ and OR. Problem 2. (10 points) The motion of a point P is given by the position vector R = 3 cos t ˆ � + t ˆ ı + 3 sin t ˆ k. Compute the velocity and the speed of P . Problem 3. (15 points: 10, 5) a) Let A = 1 2 1 3 0 1 2 1 0 ; then det( A ) = 2 and A 1 = 1 2 1 1 2 a 2 2 b 5 6 ; find a and b . x 1 b) Solve the system A X = B , where X = y and B = 2 .
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