Figure $3$ shows a $3-$D force vector with two ropes connected at the hook at point A and stretched to specific points $B$ and $C.$ A force of $70$ N and $40$ N was applied to the ropes $AB$ and $AC,$ respectively.

$($a$)$ Produce the force acting on the ropes $AB$ and $AC$ in cartesian vector form.

$[12$ Marks$]$

$($b$)$ Determine the magnitude and angle of the resultant force acting at hook $A.$

$[10$ Marks$]$

$($c$)$ Sketch the resultant force, $F_R.$

$[3$ Marks$]$

Figure $3$