During lecture 2 we noted that in cartesian coordinate system the components of a vector a = ale and of the components of the corresponding one-form āce)-a, are equal numerically, i. e., a. ai. using that fact, verify that the components of the vector cross product of the vector a - a'ē; and the vector b -b'e; are a × b = είǐkabke with eljk-ejjk numerically equal.