You are given a point $\backslash ($ A$(1\mathrm{.}5,2,3)\backslash )$ in Cartesian coordinates and a point $\backslash ($ B$(2\mathrm{.}2,1,1\mathrm{.}7)\backslash )$ in spherical coordinates. Answer the following questions:

Note: Please mention the values in radians, and to $3$ decimal places.

$1.$ Express point $\backslash ($ A $\backslash )$ in spherical coordinates: $(,,)$

$2.$ Express point $\backslash ($ B $\backslash )$ in Cartesian coordinates: $(,)$

$3.$ Calculate the dot product $\backslash ($ A $\backslash$cdot B $\backslash )($Remember its invariant across the coordinate transformations$)$:

$4.$ Calculate the vector subtraction $\backslash ($ A$-$B $\backslash )$ in both Cartesian and spherical coordinates.

$($a$)$ Cartesian:

$)($b$)$ Spherical: $($

$($

$5.$ Calculate the cross product $\backslash (\backslash$mathrm$\{$A$\}\backslash$times $\backslash$mathrm$\{$B$\}\backslash )$ in Cartesian coordinates: $($