Question

How to find euclidean distance between two vectors

Answer 1

The Euclidean distance formula finds the distance between any two points in Euclidean space.

A point in Euclidean space is also called a Euclidean vector.

You can use the Euclidean distance formula to calculate the distance between vectors of two different lengths.

For vectors of different dimension, the same principle applies.

Suppose a vector of lower dimension also exists in the higher dimensional space. You can then set all of the missing components in the lower dimensional vector to 0 so that both vectors have the same dimension. You would then use any of the mentioned distance formulas for computing the distance.

For example, consider a 2-dimensional vector A in R² with components (a1,a2), and a 3-dimensional vector B in R³ with components (b1,b2,b3).

To express A in R³, you would set its components to (a1,a2,0). Then, the Euclidean distance d between A and B can be found using the formula:

d² = (b1 - a1)² + (b2 - a2)² + (b3 - 0)²

d = sqrt((b1 - a1)² + (b2 - a2)² + b3²)

For your particular case, the components will be either 0 or 1, so all differences will be -1, 0, or 1. The squared differences will then only be 0 or 1.

If you're using integers or individual bits to represent the components, you can use simple bitwise operations instead of some arithmetic (^ means XOR or exclusive or):

d = sqrt(b1 ^ a1 + b2 ^ a2 + ... + b(n-1) ^ a(n-1) + b(n) ^ a(n))

And we're assuming the trailing components of A are 0, so the final formula will be:

d = sqrt(b1 ^ a1 + b2 ^