Re: Cross product with Mathematica

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

```In a message dated 1/19/99 5:20:10 AM, smoisan at total.net 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]

True

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

True

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}})

True

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

True