Thats nonsense! What are you using the indices for here?? In the meantime you should really know more about vectors and indices!!
I was talking about somthing like this:
and concerning ar and ar' about something like this:
Furthermore I would suggest you adopt Freds suggestion and use angles and their pseudounit degree in a more natural way. Add deg when you read in angles and for the rest let Mathcad handle the unit.