Let's assume that one needs to calculate the dot product between two 3 dimensional vectors (unit vectors) and . This can otherwise be interpreted as finding the angle between them i.e. .
Further assume that another pair of 3 dimensional unit vectors exists and . Note that one of the unit vectors is the same in both cases. The dot product between these two can also be expressed by the angle between them as .
What will be the result if I would like to add/substract these two angles +- ?
I would appreciate if someone could also explain me geometrically the implications of the addition/subtraction process. Is there any other way of expressing the result of the addition/substraction into a single term?
Thanks a lot