Hi,

Let's assume that one needs to calculate the dot product between two3 dimensional vectors(unit vectors) $\displaystyle u_1$ and $\displaystyle u_2$. This can otherwise be interpreted as finding the angle between them i.e. $\displaystyle \cos\psi_m$.

Further assume that another pair of 3 dimensional unit vectors exists $\displaystyle u_3$ and $\displaystyle u_2$. 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 $\displaystyle \cos\psi_n$.

What will be the result if I would like to add/substract these two angles $\displaystyle \cos\psi_m$ +- $\displaystyle \cos\psi_n$?

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

Regards

Alex