Problem $(2)$

Consider the following two forces

vec$(P)=306i^{}-113$vec$(j)+78j^{}kN$

vec$(Q),$ where $Q=243kN,$ angles between the line of action of $Q$ and the $x$ and $z$ axes are $55$ and $120,$ respectively.

a$)$ Find the angle between the line of action of vec$(P)$ and the $z-$axis?

b$)$ Calculate the components of vec$(Q).$

c$)$ If point $N(91,-34,23)m$ is on the line of action of vec$(P),$ calculate the moment of vec$(P)$ about point $A(2,12,7)m?$

d$)$ If point $G(139,143,-122)m$ is on the line of action of vec$(Q),$ calculate the moment of vec$(Q)$ about point $B(53,-55,19)m.$

e$)$ Find the resultant moment of vec$(P)$ and vec$(Q)$ about point $C(100,-100,300)m.$

f$)$ Calculate the resultant of vec$(P)$ and vec$(Q).$