What is the relationship between multidimensional vectors and Euclidean distance?

The relationship between multidimensional vector and Euclidean distance is that Euclidean distance is a common method to measure the absolute distance between two points in multidimensional space. Euclidean distance in two-dimensional and three-dimensional space is the distance between two points, which is extended to n-dimensional space. The formula of Euclidean distance is: $ $ d (x, y) = sqrt {sum _ {i =1} n {(x _ i-y _ i) 2}} $ where $ x = (x).