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Solution to Problem2


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Problem2:

Find three different vectors in 3D, u,v,w such that the cross product between them is not associative.

SOLUTION:


Make simple choices like,

> u := [1,0,0]: v := [0,1,0]:

and choose w arbitrary like,

> w := [a,b,c]:

Now define the LHS and the RHS of the associativity equation and we show that these are different.

> alias(cp=crossprod):

the previous aliasing is just to save typing...

> LHS := cp( cp(u,v),w );

                               LHS := [-b, a, 0]
> RHS := cp( u, cp(v,w));
                               RHS := [0, a, 0]

So LHS is different to RHS if b is chosen different from zero.


Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Mon Feb 7 14:06:37 EST 2000