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# Vector Calculus: Describing the graph of an equation

Posted on 2011-09-19
Medium Priority
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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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LVL 84

Expert Comment

ID: 36564437
do you mean

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

ID: 36564454
nope, -k, i.e. z = -1
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LVL 84

Accepted Solution

ozo earned 1000 total points
ID: 36564469
In that case, it seems like just an ellipse.
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Author Comment

ID: 36564540
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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Assisted Solution

aburr earned 1000 total points
ID: 36564935
"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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