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Message: <blockquote data-quote="jcoltea" data-source="post: 2002283" data-attributes="member: 726431">Hello all!  Our teacher gave us a difficult extra credit problem for our vector calculus class a few days ago, and I have been playing with it ever since but I can't seem to find the proper proof.  Any help would be appreciated!Suppose that the function F:[a.b] -->R^3 is a function that parametrizes a curve C (this means that F(a) = F(b)).  Suppose that P (in the set of R3) is a point not on the curve.  If Q = F(to) is a point on C that is as close to P as possible, with a<to<b.  Prove that the vectors PQ and F'(to) are perpendicular. (F'(to) is the derivative of F at to)</blockquote>