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Math Help - Multivariable calculus cylinder equation

  1. #1
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    Post Multivariable calculus cylinder equation

    I got assignment question, i didn't get how to start with.
    It is as I know the defination of cylinder..

    Q:Find the equation of cylinder if the curve is f(x , y) =0 and
    n=<a,b,c> and c not equal to zero.

    Please help me to start with
    Thanks !!
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  2. #2
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    Quote Originally Posted by rida426 View Post
    I got assignment question, i didn't get how to start with.
    It is as I know the defination of cylinder..

    Q:Find the equation of cylinder if the curve is f(x , y) =0 and
    n=<a,b,c> and c not equal to zero.
    If I understand it right, the equation f(x,y)=0 represents the cross-section of the cylinder by the plane z=0. Think of that as being some sort of curve (maybe a circle) centred at the origin. Then the cross-section of the cylinder for other values of z ought to look like the same curve, but centred at a point on the line in the direction of the vector (a,b,c).

    The point on this line having its third coordinate equal to z is \left(\tfrac acz,\tfrac bcz,z\right). That makes me think that the equation of the cylinder should be f\!\left(x-\tfrac acz, y-\tfrac bcz\right)=0. But I don't know how to give a convincing explanation of that.
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  3. #3
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    how the point on the line that is parallel to z-axis is (a/cz,b/cz,z) ??

    check me if at any point I am wrong:

    n=<a,b,c>

    line equation: r=r+tv;

    r=<x0+y0+z0> + t<a,b,c>

    z=z0, (not a fixed value i.e whole z-axis upward)

    line: x=x0+at , y=y0+bt, z=z0+ct.

    => x0=x-at, y0=y-bt, z0=z-ct ;

    t=(z-z0)/c put it in x0 and y0 equations

    x0=x- a(z-z0)/c, y0=y- b(z-z0)/c

    ???

    I am not going to the right direction I think .......
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