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MathGroup Archive 2007

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Re: Non-calculus vector math

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75779] Re: Non-calculus vector math
  • From: "David Rees" <w3bdevilREMOVE at THISw3bdevil.com>
  • Date: Thu, 10 May 2007 05:18:17 -0400 (EDT)
  • References: <200705080952.FAA18614@smc.vnet.net> <f1s17f$f7r$1@smc.vnet.net>

Lovely, thanks all :)

"Murray Eisenberg" <murray at math.umass.edu> wrote in message 
news:f1s17f$f7r$1 at smc.vnet.net...
> Since a vector in Mathematica may be represented by a list, such vector
> algebra is just adding lists and multiplying lists by numbers.  So you
> can work your problem essentially the same way you would with paper and
> pencil (except that you use braces to enclose a list instead of
>
> Easy:
>
>   x0 = {3,6,-1}; v = 1000{1,-4,5};
>   x0 + 35 v
> {35003,-139994,174999}
>
> Or, if you'd like to use units:
>
>   <<Units`  (* load package *)
>   x0 = {3, 6, -1}; v = {1, -4, 5}/SI[Milli Second];
>   x0 + 35 Second v
> {35003,-139994,174999}
>
> In both cases, there was no actual need to give names to the initial
> position position or velocity; I used names only in order to clarify
> what was being done.  (You might also introduce a name for the time, say
> t1.)
>
> Notice that the above did not use the x i + y j + z k format. If you
> want that, you can do it.  Start with
>
>   {i,j,k}={{1,0,0},{0,1,0},{0,0,1}};
>
> or, in Mathematica 6.0:
>
>   {i, j, k} = UnitVector[3, #] & /@ {1, 2, 3};
>
> (Probably you would not want to usurp the letters i,j,k for this, since
> they are so useful as counters, so it would be a better idea to use,
> say, DoubleStruckI, DoubleStruckJ, DoubleStruckK.  I cannot display
> those in this plain-text message without going to Unicode, so I'm not
> using them.)
>
> Then instead of the above you could calculate:
>
>   x0=3i+6j-k; v=1000(i-4j+5k);
>   x0+35v
>
> (or you could again do it with units).  With a bit more work, you could
> display the result in the x i + y j + z k form.
>
> David Rees wrote:
>> Ahoy,
>>
>> How can I perform elementary vector math in Mathematica? From what I've
>> found, it's all Vector Calculus, but what about trivial/elementary vector
>> math?
>>
>> Things like: "Particle A with position unit-vector of (3i+6j-1k) and
>> velocity vector (1i-4j+5k)ms^-1 collides with Particle B 35 seconds after
>> moving off from its initial position, where did it collide?"
>>
>> Thanks
>>
>>
>>
>
> -- 
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305
> 




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