Problem #$7(35$ points$)$: The tower crane is exerting a tension in cable AB of $10$ kN applied to point $A.$ Coordinates for points $A,B,$ and $O$ are: $A=(0,18,30),B=(6,13,0),$ and $,0).$ Calculate the following quantities:

$($a$)$ The position vector $AB$

$($b$)$ The direction cosine angles $(,,)$ for vector $AB$

$($c$)$ The tension force $T$ acting at point $A($write T as a $3$D Cartesian vector$)$

$($d$)$ The moment $M_0$ of tension $T$ about point $O$ at the base of the tower crane