Please answer carefully and explain the maths result. Reconsider this data set with $5$ vectors and $3$ variables:

Assume a set of two different clusters, $C=\{C_1,C_2\},$ where

$C_1=\{x^{(1)},x^{(2)},x^{(3)}\}$ and $C_2=\{x^{(4)},x^{(5)}\}.$

Compute the centroids and inertia of $C_1$ and $C_2.$ Then,

compute the WCSS of $C.$ Also compute the squared Euclidean

distance between the two centroids $($do not use normalisation$).$