The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I have two of these vectors each with 80 rows, does the angle between these vectors have any physical significance? Should I think of the vector to mean there are 80 dimensions, one dimension for each of the 80 A/D conversions? (My application is trying to estimate the phase/frequency of the sine wave.) Thanks!