$2-$ Given three vectors, $A=4i-5j-8k,B=2i-3j-k$ and $C=i-j+k$

Evaluate: $($a$)A(B+C)=(AB)+(AC)$

$($b$)A*(B+C)$

$($c$)A-3B+C$

$($d$)A+C-B$

$3.($a$)$ A projectile is fired horizontally from a gun that is $20$ m above flat ground, emerging from the gun with a speed of $25\frac{m}{s}.$ At what horizontal distance from the firing point does it strike the ground?

$($b$)$ A force of $50$ N is used to pusin a box through a distance $2\mathrm{.}4$ m $.$ A work of $45$ J was done on the box.

$($i$)$ What is the direction of the force?

$($ii$)$ Find the mass of the box if the velocity is $2\frac{m}{s}$