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mobius70
Joined: 24 Jan 2008
Posts: 19
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| Posted: Mon Mar 10, 2008 12:04 pm Post subject: Another 3-D Question |
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| 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
Joined: 04 Dec 2007
Posts: 46
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| Posted: Fri Mar 14, 2008 11:29 pm Post subject: |
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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:
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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