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Vector Calculus, Unit normal to surface help

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    If [itex]\phi[/itex](x,y,z) = x3 + 2xy +yz3 find [itex]\nabla[/itex][itex]\phi[/itex] at the point P=(1,1,2) and direction of the unit normal to the surface [itex]\phi[/itex](x,y,z) = 11 at P.

    2. Relevant equations



    3. The attempt at a solution
    Worked out [itex]\nabla[/itex][itex]\phi[/itex] to be 5i + 10j + 12k
    Got |[itex]\nabla[/itex][itex]\phi[/itex]|= √256

    so the unit normal to surface is surely [itex]\frac{5+10+12}{√269}[/itex]
    but how does the =11 bit make a difference?

    Thanksss
     
    Last edited: Apr 10, 2012
  2. jcsd
  3. Apr 10, 2012 #2

    tiny-tim

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    welcome to pf!

    hi tarwe! welcome to pf! :smile:
    it doesn't :wink:

    (btw, it's not 256)
     
  4. Apr 10, 2012 #3
    Re: welcome to pf!


    thank you!
    that was a typo, meant 269, was thinking in binary :/
     
  5. Apr 10, 2012 #4

    HallsofIvy

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    You mean [itex]\frac{5i+10j+12k}{√269}[/itex]

    It would change the exact position but not the normal to the surface.

     
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