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Unformatted text preview: where it is largest and smallest. Hint: It is easier to work with the square of the speed. Problem 4. 1 2 3 1 1 4 1 1 M = 3 2 1 M = a 7 8 12 2 1 1 b 5 4 (a) (5) Compute the determinant of M . b) (10) Find the numbers a and b in the formula for the matrix M 1 . x + 2 y + 3 z = 0 c) (10) Find the solution r = x, y, z to 3 x + 2 y + z = t as a function of t . 2 x y z = 3 d r d) (5) Compute . 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 x 3 y 2 z = 6 in vector notation as an equation involving r and the normal vector to the plane. d r (b) (5) By dierentiating your answer to (a), show that is perpendicular to the normal vector dt to the plane....
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This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.
- Spring '08
- Multivariable Calculus