I think you should give some more info to get an answer you can use.
What kind of vectors?
Do you have two pairs of complex numbers or two analog voltages ??
Regards Uwe
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For φ: I would use
a zero crossing comparator to get the phase signals of U1 and U2 and
then make a time measurement of a) the signal period and b) the delay
U1 to U2.
Regards Uwe
__________________
The sum of intelligence on earth is a constant. And the population grows and grows and .....