Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table.

$\backslash$table$[[$Characteristic$,$Cluster $1,$Cluster $2,$Cluster $3],[$Alcohol$,0\mathrm{.}819,0\mathrm{.}164,-0\mathrm{.}937],[$MalicAcid$,-0\mathrm{.}329,0\mathrm{.}869,-0\mathrm{.}368],[$Ash$,0\mathrm{.}248,0\mathrm{.}186,-0\mathrm{.}393],[$Alcalinity$,-0\mathrm{.}677,0\mathrm{.}523,0\mathrm{.}249],[$Magnesium$,0\mathrm{.}643,-0\mathrm{.}075,-0\mathrm{.}573],[$Phenols$,0\mathrm{.}825,0\mathrm{.}977,-0\mathrm{.}034],[$Flavanoids$,0\mathrm{.}896,-1\mathrm{.}212,0\mathrm{.}083],[$Nonflavanoids$,-0\mathrm{.}595,0\mathrm{.}724,0\mathrm{.}009],[$Proanthocyanins$,0\mathrm{.}619,-0\mathrm{.}778,0\mathrm{.}010],[$Colorlntensity$,0\mathrm{.}135,0\mathrm{.}939,-0\mathrm{.}881],[$Hue$,0\mathrm{.}497,-1\mathrm{.}162,0\mathrm{.}437],[$Dilution$,0\mathrm{.}744,-1\mathrm{.}289,0\mathrm{.}295],[$Proline$,1\mathrm{.}117,-0\mathrm{.}406,-0\mathrm{.}776]]$

Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations.

Characteristic

$\backslash$table$[[$Alcohol$,-1\mathrm{.}023],[$MalicAcid$,-0\mathrm{.}480],[$Ash$,0\mathrm{.}049],[$Alcalinity$,0\mathrm{.}600],[$Magnesium$,-1\mathrm{.}242],[$Phenols$,1\mathrm{.}094],[$Flavanoids$,0\mathrm{.}001],[$Nonflavanoids$,0\mathrm{.}548],[$Proanthocyanins$,-0\mathrm{.}229],[$Colorlntensity$,-0\mathrm{.}797],[$Hue$,0\mathrm{.}711],[$Dilution$,-0\mathrm{.}425],[$Proline$,0\mathrm{.}010]]$

If required, round your answers to three decimal places. Do not round intermediate calculations.

Distance from new wine and Cluster $1$:

Distance from new wine and Cluster $2$:

Distance from new wine and Cluster $3$:

Select your answer $-vv$ is the most appropriate for the new wine observation.