Cross Product. Is there any other basis than the Right Hand Rule when determining the direction of the Cross Product?
Is there a Mathematical or Scientific, or any explanation/proof that points the direction of the Cross Product?
9 x 23 sin(30) = 108 1/2 = 54... Ok, So I got c = 54... but doesn't tell what direction, just basing on the Right Hand Rule.
One way to define the cross product is to declare that $a\times b$ is the unique vector such that for every $c$: $$ (a\times b) \cdot c = \det [a,b,c]$$ This defines the components, whence the direction, of $a \times b$ uniquely, e.g. $(a\times b)_z=a_xb_y-a_yb_x$, etc... But of course this leaves the definition of direction in the hands of $\det(\cdot)$.