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Parametrising a curve

  1. Mar 19, 2006 #1
    hi, I'm stuck on a curve parametrisation question. It reads as follows:

    "Consider the two spherical surfaces [itex]x^2 + y^2 + z^2 = 4[/itex] and [itex]x^2 + y^2 + (z - 1)^2 = 2[/itex]. Let [itex]\gamma[/itex] be the curve in which they meet. Evaluate the line integral x over gamma "

    So far I have let the two surfaces equal one another and found that [itex] z = \frac {3} {2}[/itex]. Then I substituted this back in to the equation above and found that [itex] y = \sqrt {\frac {7} {4} - x^2} [/itex].

    I don't quite know how to take this further and parametrise the curve between the two spheres.

    I'm not sure if this is the right way of doing this. Any help or comments would be appreciated.

    Last edited: Mar 19, 2006
  2. jcsd
  3. Mar 19, 2006 #2


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    You have, in other words
    z = 3/2
    x^2 + y^2 = 7/4

    In a plane parallel to the xy-plane, you can recognize the second equation as a circle with radius sqrt(7/4). And the z-coordinate of this circle is 3/2. Do you know the parametric equation for a circle with a given radius r? That's what you put in your xy-coordinates for the curve. In your z-coordinate you already know what to put.
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