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Unformatted text preview: i (b) r ( t ) = e t ; p 2 t;e t (c) r ( t ) = h e t cos t;e t sin t;e t i Problem 4. Section 14.4 For each of the following problems, you are given the accelleration function of a particle moving in R 3 as well as its initial position and velocity. Find its position at time t . (a) a ( t ) = h ; ; 1 i , r (0) = h 2 ; 1 ; 1 i , v (0) = h 3 ; 1 ; 1 i (b) a ( t ) = h e t ; sin t; cos t i , r (0) = h 1 ; ; 1 i , v (0) = h ; 2 ; 2 i Problem 5. Challenge Problem (will not be graded): Given a curve r ( t ) parameterized by arclength, dene the binormal vector of r ( t ) to be B ( t ) = N ( t ) T(t) where T is the unit tangent and N is the unit normal. Show that B is a multiple N at every point on the curve, and show that the curve lies on a plane in R 3 if and only if B = 0 . 1...
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This note was uploaded on 03/20/2010 for the course MATH 230 at Pennsylvania State University, University Park.