Find Unit Vector perpendicular to the Surface

  1. Find Unit Vector perpendicular to the Surface,

    x3+zx=1 at the point P=(1,2,-1)

    I figures that the perpendicular vector would be,

    N(X)=grad(x3+zx)
    = (3x2+z, 0, x)
    N(P)= (3,0,1)
    Then the unit vector would be,

    n=N(P)/||N(P)||

    n=(3/51/2,0,1/51/2)
    The answer i get is not the right answer and i dont see where im going wrong.

    Thanks,
     
  2. jcsd
  3. Dick

    Dick 25,738
    Science Advisor
    Homework Helper

    Is (3x^2+z,0,x) at P=(1,2,-1) really (3,0,1)?
     
  4. Thanks for pointing that out Dick, minor error.

    (2,0,1)

    Its still not the right answer which is 1/271/2(5,1,1)
     
  5. Dick

    Dick 25,738
    Science Advisor
    Homework Helper

    Then there's probably a typo in the problem. The surface x^3+zx=1 equation doesn't have a 'y' in it. That means the y direction is tangent to the surface. The normal vector can't possibly have a nonzero y component.
     
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