prac1a - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 2007 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 ² ² ² ² ² ² ² ² ² 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 ² ; then det( A ) = 2 and A 1 = 1 2 ± 1 1 2 a 2 2 b 5 6 ² ; find a and b . x 1 ² ² b) Solve the system A X = B , where X = ± y and B = ± 2 . z
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prac1a - MIT OpenCourseWare http:/ocw.mit.edu 18.02...

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