Features of Vector Product
It is easy to verify by using your right hand that
a x b = - b x a, and it’s obvious that a x a = 0.
For the unit vectors i, j, k, there exist relations such as
i x j = k, j x k = i, k x i = j, and i x i = 0, j x j = 0, k x k =0.
The components of c = a x b are