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Vector Calculus: Describing the graph of an equation

Posted on 2011-09-19
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Describe the graph of the equation:

r = 3cos(t) i + 2sin(t) j - k



I figured it out to be a elliptic cylinder in 3-space, but apparently it's not right? I was reading my book and it said something about being a helix but it does a terrible job explaining how it came to that conclusion. Any help is appreciated.
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Question by:Zenoture
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by:ozo
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do you mean

r = 3cos(t) i + 2sin(t) j - k*t
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by:Zenoture
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nope, -k, i.e. z = -1
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ozo earned 250 total points
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In that case, it seems like just an ellipse.
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by:Zenoture
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Yeah, on the plane z = -1

But how do I sketch that so it actually looks like it should? I'm terrible at drawing...
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by:aburr
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"But how do I sketch that so it actually looks like it should?"
by putting a t in front of the k as ozo suggested.
Forget the k part for starters. What do you have? You have the end of the vector tracing out an ellipse.
Now put in the -K (unit vector in the z direction) What do you have? The ellipse drawn at -1 in the z direction.
That is not a helix.
Correct the misprint as ozo suggested. What do you now have? You have the point of the vector still going in its ellipse but now it is sinking steadily in the - z direction yielding the required helix.
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