If your solution to stated problem does not match the given solution, you should self-critique per instructions at

   http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution.  If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.  This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

At the end of this document, after the qa problems (which provide you with questions and solutions), there is a series of Questions, Problems and Exercises. 

query_10_4

Question:   Find T(t) and N(t) when R(t) = (e^-2t cost)i + (e^-2t sint )j + e^(-2t) k.

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Question:  Find the curvature of the plane curve y = sin (-3x) at x = pi/2.

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Question:  Let C be the curve given by R(t) = (1-cos t)i + (t-sin t)j + (4sin(t/2))k

• Find the unit tangent vector T(t) to C
• Find dT/ds and the curvature k(t)

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Question:  Find the maximum curvature for the curve y = e^3x.

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Question:  If T and N are the unit tangent and normal vectors on the trajectory of a moving body, we can define B = T X N to be the unit binormal vector. A coordinate system with three planes can be made at each point with these vectors since they are mutually orthogonal.

• Show that T is orthogonal to dB/ds (Hint: Differentiate B dot T)
• Show that B is orthogonal to dB/ds (Hint: Differentiate B dot B)
• Show that dB/ds = -(tau)N for some constant tau. (We call the constant tau the torsion of the trajectory)
• **Prove the Frenet-Serret formulas: (dT/ds = kN, dN/ds = -kT + tauB, dB/ds = -tauN). Where k is the curvature and tau = tau(s) is a scalar function.

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