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Re: Cross product with Mathematica

  • To: mathgroup at
  • Subject: [mg15563] Re: [mg15521] Cross product with Mathematica
  • From: BobHanlon at
  • Date: Tue, 26 Jan 1999 13:44:43 -0500 (EST)
  • Sender: owner-wri-mathgroup at

In a message dated 1/19/99 5:20:10 AM, smoisan at writes:

>I wanted to do some calculations involving cross product over the
>weekend using Mathematica.  That's when I discovered there's no way of
>doing any cross product using this software, at least, not in the
>version we have at the univerity which is 2.2 for Solaris.  Is this
>possible in another version?
> Is there an add-on available somewhere so I can do cross product?  Any
>help would be appreciated.

Use the built-in function Cross

u1 = {x1, y1, z1};
u2 = {x2, y2, z2};
w = Cross[u1, u2]

{y1*z2 - y2*z1, x2*z1 - x1*z2, x1*y2 - x2*y1}

w == -Cross[u2, u1]


{Dot[u1, w], Dot[u2, w]} == {0, 0} // Simplify


Clear[i, j, k];
w == (Det[{{i,j,k}, u1, u2}] /. 
	{{i->1, j->0, k->0},
		{i->0, j->1, k->0},
		{i->0, j->0, k->1}})


w == (D[Det[{{i,j,k}, u1, u2}], #]& /@ {i, j, k})


or define your own function

xProd[{x1_, y1_, z1_}, {x2_, y2_, z2_}] := 
		{y1*z2 - y2*z1, x2*z1 - x1*z2, x1*y2 - x2*y1};

Bob Hanlon

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