Although I can't answer your question, I can see that, because you submitted it twice, you are seeking a solution quickly.
I'm puzzled about U, the unit vector. Does aA represent a cross-product of a and A? It can't be a dot product because U is described as a vector, not a scalar. The cross product would then appear to produce units of square metres, and why then would U be a unit vector? Both a and A are defined as vectors, but are we defining U as the product of the magnitudes of a and A and in which direction would be the unit vector? I appreciate i, j and k are unit vectors, but I don't follow how U is a unit vector. Can you explain these points for other users?