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Vector analysis prob

  1. Feb 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Schaum's vector analysis prob 4.65
    Find the values of constants a,b,c so that directional derivative of phi=axy^2+byz+cz^2x^3 at (1,2,-1) has a maximum of magnitude 64 in a direction parallel to the z axis.


    2. Relevant equations



    3. The attempt at a solution
    Directional derivative is maximum along grad(phi). After taking grad(phi) at (1,2,-1) I got
    (4a+3c)i+(4a-b)j+(2b-2c)k
    I don't know how to make use of the 'direction parallel to z axis' condition.
     
  2. jcsd
  3. Feb 26, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    If grad(phi) is maximum in Z-axis, it may be zero in x and y-axis. Then
    (2b - 2c) = 64.
    (4a+3c) = (4a-b) = 0.
    Solve these equations to find a, b and c.
     
  4. Feb 26, 2010 #3
    Got it! Thanks.
     
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