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Math Help - [SOLVED] Unit normal to the surface point

  1. #1
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    [SOLVED] Unit normal to the surface point

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    Last edited by Chris0724; March 15th 2009 at 10:00 AM.
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  2. #2
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    Quote Originally Posted by Chris0724 View Post
    Surface parametric equation given as ,

    r (u,v) = v^2 i - uv j + u^2 k ,

    bounded by 0 < u < 3 ; -3 < v < 3

    1. Find unit normal to the surface point (4 ,-2 , 1 )
    -----------------------------------------------------------------------
    i differentiate r with respect to u and achieve ( 0 , -v , 2u ) --- eqn 1
    i differentiate r with respect to v and achieve ( 2v , -u , 0 ) ---- eqn 2

    at point (4 ,-2 , 1 ),

    ( v^2 = 4 , -uv = -2 , u^2 = 1 ) ,<---- i like to ask if this step is correct?

    v = 2 , u = 1

    sub in the u & v values to eqn 1 & 2 and cross the 2 vector to achieve normal vector....


    many thanks!

    Yes, becuase if you take the negative root for V it forces u=-1, and that value is not in the domain of your function.
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