Hello folks! I'd be happy for any help you could give me. Thanks! :)(adsbygoogle = window.adsbygoogle || []).push({});

First though I'd like to make clear that I want to solve this problem myself, even if something seems obvious to you and you feel there is no harm in making a certain logical leap - please take the time to consider whether or not it's a step which I should be working out myself. I have very little background in Calc. and it took me a while just to place this problem when digging through my old texts from uni, but I would like to understand what the concepts I'm dealing with are.

Here is the original question: (Everything else that follows are notes that I have tracked down on the net to help me understand it.)

This was all that was presented. Is this a matrix then? The spacing does not seem to indicate something as simple as f(t)=(5-3t); g(t)=(5-2t); h(t)=(-4-2t); but I don't want to make any assumptions. Starting from the point (5, 5, -4), reparametrize the curve: r(t) = ( 5 -3 t )i + ( 5 -2 t )j + ( -4 -2 t )k in terms of arclength

I'm really quite at a loss as to where to start. In simple terms it seems that I really haven't gotten anywhere yet and must still:

1. Figure out what ( 5 -3 t )i + ( 5 -2 t )j + ( -4 -2 t )k represent in a way that I can understand what I'm working with.

2. Find the arclength.

3. Reparametrize.

I'm assuming the relationship between the point given and the curve is one where by the question is supposed to be that much similar. Something akin to t=0 or something?

Other notes I picked up and which I'm still digesting:

A vector function of a single variable is much like a parametrized curve,

f(t)=f1(t)i+f2(t)j+f3(t)k

(where i, j, k, are the vectors (1,0,0), (0,1,0), and (0,0,1), respectively)

The functions fi are the component functions and much of calculus of vector functions of one variable is done by components, for example,

f'(t)=f1'(t)i+f2'(t)j+f3'(t)k

A curve is simply defined as a vector function of a single variable:

r(t)=x(t)i+y(t)j+z(t)k

http://planetmath.org/encyclopedia/SpaceCurve.html [Broken]

http://rsp.math.brandeis.edu/Generi.../Documentation/DocumentationPages/Curves.html (Documentation for 3D-XplorMath)

http://oregonstate.edu/dept/math/CalculusQuestStudyGuides/vcalc/arc/arc.html

Thanks for any help you can give! I'm quite in the dark.

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# Reparametrizing a space curve in terms of arclength:

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