Unformatted text preview: t = 0, the rear bumper is at (1 , 0).) b) (10) Compute the speed of the bug, and nd where it is largest and smallest. Hint: It is easier to work with the square of the speed. Problem 4. M = 1 2 3 3 2 1 211 M1 = 1 12 1 1 4 a 78 b5 4 (a) (5) Compute the determinant of M . b) (10) Find the numbers a and b in the formula for the matrix M1 . c) (10) Find the solution ~ r = h x, y, z i to x + 2 y + 3 z = 0 3 x + 2 y + z = t 2 xyz = 3 as a function of t . d) (5) Compute d~ r dt . Problem 5. (a) (5) Let P ( t ) be a point with position vector ~ r ( t ). Express the property that P ( t ) lies on the plane 4 x3 y2 z = 6 in vector notation as an equation involving ~ r and the normal vector to the plane. (b) (5) By dierentiating your answer to (a), show that d~ r dt is perpendicular to the normal vector to the plane....
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 Fall '08
 Auroux
 vw, rear bumper, normal vector dt, 1 2 3 1 M, plane. dr

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