These words are often used wrongly and very often unnecessarily. "Of ten sentences in which they occur", says Fowler, "nine would be improved by their removal". Here is a recent example:
There are many other provisions in the Act which are referred to in the respective chapters dealing with the main fields of activity of the Central Authority and the Area Boards.
They have only one useful function. That is to serve as distributors in such a sentence as:
Please fill in both the buff and the green forms, and return them to the Ministry and the Committee respectively.
Without the respectively it would not be clear which authority preferred which colour. But even here the word could be dispensed with and the style of the sentence improved by writing:
Please fill in both forms and return the buff one to the Ministry and the green one to the Committee.
There is also a harmless but unnecessary distributive use in such a sentence as:
Local Education Authorities should survey the needs of their respective areas....
It hardly seems necessary to guard against the risk that Local Authorities might think that they were being told to survey one another's areas. Anyway it is neater to write "Each Local Authority should survey the needs of its area".