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Check if I did this problem correctly please

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data

    Check that the point (-1,1,2) lies on the given surface. Then find a vector normal to the surface and an equation for the tangent plane to the surface at (-1,1,2).

    z=x2 + y2


    2. Relevant equations



    3. The attempt at a solution

    (2) = (-1)2 + (1)2

    2 = 2; (-1, 1, 2) lies on the surface z=x2 + y2

    ----------

    0 = -z + x2 + y2
    f(x,y,z) = -z + x2 + y2

    ∇f = <2x, 2y, -1>
    ∇f (-1,1,2) = <-2,2,-1>

    tangent plane: -2(x+1) + 2(y-1) - (z-2) = 0

    -2x + -2 + 2y - 2 - z + 2 = 0

    -2x + 2y - z = 2 <------- Tangent plane equation

    normal line: < -2, 2, -1>

    as unit vector: (1/√3) <-2, 2, -1>

    Did I do this correctly?
     
  2. jcsd
  3. Oct 16, 2013 #2
    It looks right to me.
     
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