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Equation of tangent plane to surface and parametric equations to normal line question

  1. Feb 23, 2012 #1

    s3a

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    I'm attaching the question, answer, and my work. My work is almost 100% correct except that there are two coefficients of t that are supposed to be positive instead of negative and I marked those with red writing and would appreciate an explanation as to why this is the case.

    Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Feb 23, 2012 #2
    Re: Equation of tangent plane to surface and parametric equations to normal line ques

    You have a sign error because you forgot to transform the equation in its (f(x,y,z)=0 form
    that is, from the first formula you must substract z
    that would give you the function F(x,y,z)=x²+2xy+5y²+x+3y+1-z
    (notice that z changes sign which is what did not happen in your solution)
    if you continue from there, you will get to a solution identical to the known answer (except maybe t will have a minus sign, but everywhere, so it doesn't change anything)

    Cheers...
     
  4. Feb 23, 2012 #3

    Mark44

    Staff: Mentor

    Re: Equation of tangent plane to surface and parametric equations to normal line ques

    For your tangent plane you have z = -13x - 43y - 112. You can also write this in standard form as 13x + 43y + z = -12. From this form, a normal vector can be obtained by inspection: <13, 43, 1>.
     
  5. Feb 23, 2012 #4

    s3a

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    Re: Equation of tangent plane to surface and parametric equations to normal line ques

    Thanks guys, I get it now! :)
     
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