Given,

$X_1=(1,2,2)$

$X_2=(2,5,3)$

To find -

(i) Manhattan distance

(ii) Euclidean distance

(i) Manhattan distance -

As we know,

$d = \sum^{n}_{i=1} |x_i - y_i|$

Here, = | 1 - 2 | + | 2 - 5 | + | 2 - 3 |

= 1 + 3 + 1

= 5.

(ii) Euclidean distance -

As we know,

$d = \sqrt{ \sum^{n}_{i=1} |x_i - y_i|^{2}}$

Here, $\sqrt{(1 - 2)^2 + (2 - 5)^2 + (2 - 3)^2 }$

$=\ \sqrt{1 + 9 + 1}$

$=\ \sqrt {11}$

= 3.316. Ans.