QUESTION $1[10$ MARKS$]$

Two forces $F_{AB}(100N)$ and $F_{AC}(120N)$ are acting on a particle as shown in Figure $1.$

$($a$)$ Express $F_{AB}$ and $F_{AC}$ as Cartesian vectors.

$[4$ marks$]$

$($b$)$ Determine the magnitude and coordinate direction angles of resultant force. $[4$ marks$]$

$($c$)$ Determine the angle between the two forces $F_{AB}$ and $F_{AC}.$

$[2$ marks$]$

Figure $1$: A particle exerted by two force