Vector

A vector are elements that can be added together and scaled by a constant. It is represented as a list of numbers. The dimension of a vector is the number of elements in the list. An example of a vector of size 3.

$$\begin{pmatrix} 1 \\ 4 \\ 7 \end{pmatrix}$$

Vectors can be through of as points in a high dimensional space. You can compute the $L_2$ distance (meaning regular distance) between vectors using the formula (for 2 vectors of the same size $a$ and $b$):

$$d = \sqrt{(a*x - b_x)^2 + (a_z - b_z)^2 + (a_z - b_z)^2}$$

Or, in general, for vectors with $n$ dimensions:

$$d = \sqrt{\sum^{n}*{i=0} (a_i - b_i)^2}$$

Or, even more in general, you can compute the $L_k$ distance (with $k \geq 1$) as:

$$d_k = \biggl(\sum^{n}_{i=0} (a_i - b_i)^k\biggr)^{1/k}$$