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Problem #$1(30$ points$)$: The force $F$ of magnitude $80$ lb acts at the end of the pipe assembly at point B $,$ and is directed along the line BC as shown. Coordinates for points $A,B,$ and C are given as follows: $A=(0,1,0),B=(2,3,-1),$ and $C=(2,0,0).$ Determine the following quantities:

$($a$)$ The $x,y,$ and z components of force $F.$

$($b$)$ The angle between force $F$ and pipe BA$.$

$($c$)$ The moment $M_A($vector$)$ of force $F$ about point A$.$