TITLE: Solution to Problem2
# !b1 Problem2:
Find three different vectors in 3D, u,v,w such that the cross product
between them is not associative.

!b3 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.

>