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Homework Help: Vector analysis problem

  1. Aug 12, 2010 #1
    1. The problem statement, all variables and given/known data
    The temperature at a point (x,y,z) in space is given by
    T(x,y,z) = x^2+y^2-z. a mosquito located at (1,1,2) desires to fly in such a direction that it will get warm as soon as possible. in what direction should it fly?

    2. Relevant equations
    Grad T = Txi+Tyj+Tkz


    3. The attempt at a solution
    i first take its grad T = 2xi+2yj-k

    then for direction i just get its unit vector.... that is 1/3(2xi+2yj-k) ..

    am i right or wrong
     
  2. jcsd
  3. Aug 16, 2010 #2

    lanedance

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    looks ok to me
     
  4. Aug 16, 2010 #3

    Mark44

    Staff: Mentor

    You didn't use the information that the mosquito starts at (1, 1, 2). Also, why do you think that (1/3)(2xi + 2yj - k) is a unit vector?
     
  5. Aug 17, 2010 #4

    HallsofIvy

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    Science Advisor

    How did a problem involving the gradient of a vector function get into the "Precalculus Homework" section? I'm going to move this to the "Calculus and beyond" section.

    (1/3)(2i+ 2j- k) is a unit vector. Whether or not (1/3)(2xi+ 2yj- k) is depends upon the values of x and y.
     
  6. Aug 17, 2010 #5

    lanedance

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    Homework Helper

    sorry, looked a little quickly & got the jist of it - all good pick-ups
     
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