       Re: Non-calculus vector math

• To: mathgroup at smc.vnet.net
• Subject: [mg75712] Re: [mg75668] Non-calculus vector math
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 9 May 2007 04:26:30 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200705080952.FAA18614@smc.vnet.net>
• Reply-to: murray at math.umass.edu

```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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