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. |