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Unformatted text preview: 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 , , k. O Q 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 + 3 sin t + t k. Compute the velocity and the speed of P . Problem 3. (15 points: 10, 5) a) Let A = 1 3 2 2- 1 1 1 ; then det( A ) = 2 and A- 1 = 1 2 1 a b- 1- 2 5 2 2- 6 ; find a and b . b) Solve the system A X = B , where X = x y z and B = 1- 2 1 . c) In the matrix A , replace the entry 2 in the upper-right corner by c . Find a value of c for which the resulting matrix M is not invertible....
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This note was uploaded on 04/18/2008 for the course 18 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08