Fortran (GFortran), 85 bytes

subroutine d(A,n,e);real A(n,2);s=0;do 5 i=1,n;s=s+(A(i,1)-A(i,2))**2 5 e=sqrt(s);end 

Try it online!. Instead of two vectors, I read all the data into two rows of array A. But Fortran 'helpfully' stores matrices by column so when I call the procedure A is transposed. Using line number 5 instead of enddo saves 2 bytes :)

Fortran (GFortran), 85 80 bytes

function d(A,n);real A(n,2);s=0;do5 i=1,n;s=s+(A(i,1)-A(i,2))**2 5 d=sqrt(s);end 

Try it online!   _{85 bytes}

Instead of two vectors, I read all the data into two rows of array A. But Fortran 'helpfully' stores matrices by column so when I call the procedure A is transposed.
_{Using line number 5 instead of enddo saves 2 bytes :)
Saved 5 bytes using function instead of subroutine}