Do not confuse the problem of finding the length of a line segment if you know the two end points
with finding the length of a vector.
Suppose we have 2 points A(8,3) and B(11,7)
then vector AB = [3,4]
and │AB│ = √(3^2+4^2)
line segment AB = √((11-8)^2 + (7-3)^2)
when you write vector [a,b], and vectors can be drawn anywhere as long as they have the same direction and magnitude, one can assume the vector [a,b] to start at the origin (0,0) and end at the point(a,b).
Hence we can say │[a,b]│ = √(a^2+b^2)
in other words │[3,2]│ = √(9+4) = √13