Another 3-D Question

Forum for the GRE subject test in mathematics.
mobius70
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Joined: Thu Jan 24, 2008 1:11 am

Another 3-D Question

Postby mobius70 » Mon Mar 10, 2008 8:04 am

What is the equation of a cylinder in 3-D, given that its axis passes through point (a,b,c) and the orientation of the axis is along vector (l,m,n) . Assume radius of cylinder to be unity.

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lime
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Joined: Tue Dec 04, 2007 2:11 am

Postby lime » Fri Mar 14, 2008 7:29 pm

Setting the radius to 1 doesn't really simplify a problem. Therefore, we can try to get the general solution for an arbitrary radius. Apparently the locus of this cylinder will be the set of points in the space the distance from which to the axis will be equal to the radius given. Considering the point (x,y,z) as the one that would satisfy the equation of this locus we would have:
Image
If the given vector is the unit vector, it will obviously make the equation less bulky, by eliminating the denominator in the fraction.




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