face recognition by Euclidean space distance seeking for help

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In the n dimensional Euclidean space,

If The first point is P1 [x1,x2,...,xn]

The second point is P2 [y1,y2,...,yn]

so ，the Euclidean space distance from P1 to P2 is

d(P1,P2) = sqrt ( (x1-y1)^2 + (x2-y2)^2 + ... + (xn-yn)^2 )

so , in the face recognition field , for example , in many open source ， every point have x coordinate value and y coordinate value ,

I think it is ,

The first face is P1 [(x1,y1),(x2,y2),...,(xn,yn)]

The second face is P2 [(a1,b1),(a2,b2),...,(an,bn)]

so ，the Euclidean space distance from P1 to P2 is ________________________________ ?

the result is too complex , even is unsolvable .

I don't know if I have a problem with my understanding ?