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Math Help - Vector calculus problem

  1. #1
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    Vector calculus problem

    The parametric surface shown in figure 1 hasgrid curves which can be shown to be circles when is constant
    x=(2+sin(v))cos(u)
    y=(2+sin(v))sin(u)
    z=u+cos(v)
    find the center and radius of the circle at u=pi
    please help me Vector calculus problem-untitled.jpg
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  2. #2
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    Re: Vector calculus problem

    Quote Originally Posted by milad83 View Post
    The parametric surface shown in figure 1 hasgrid curves which can be shown to be circles when is constant
    x=(2+sin(v))cos(u)
    y=(2+sin(v))sin(u)
    z=u+cos(v)
    find the center and radius of the circle at u=pi
    please help me Click image for larger version. 

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    1. Plug in u = \pi. You'll get the vector:

    \langle x,y,z \rangle = \langle -\sin(v) - 2, 0, \cos(v) + \pi  \rangle

    2. From

    x= -\sin(v) - 2~\implies~x+2=-\sin(v) ...... and

    z = \cos(v)+\pi~\implies~ z-\pi = \cos(v)

    you'll get by squaring:

    (x+2)^2 + (z-\pi)^2 = (-\sin(v))^2+(\cos(v))^2 = 1

    3. This is the equation of a circle in the x-z-plane with C(-2, 0, \pi) and r = 1
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