ecko={0,y*x*z,0};
hacko={0,0,x+y+z};

D[ecko\[Cross]hacko,x]

ecko={x+y,y*x*z,(x^y)};
hacko={x+z,x*z,x+y+z};

Div[ecko\[Cross]hacko,{x,y,z}]