Problem H$02-02[$Points: $1/3]$

For the pipe assembly shown, compute the following:

$($a$)[$Points $\frac{0\mathrm{.}5}{3}$ The vector of the projection $($shadow$)$ of forces $F_1=10lbf,F_2=20lbf,$ and $F_3=30lbf$ along pipe $)=(F_{A0x}i+F_{A0}j+F_{A02}k.$ Note how $F_{A0}=F_{A01}+F_{A02}+F_{A03}.$

$($b$)[$Points $\frac{0\mathrm{.}2}{3}]$ The angle ${}_{F20A}$ between $F_2$ and pipe $0-$A via the dot product definition.

$($c$)[$Points $\frac{0\mathrm{.}1}{3}$ Compute the direction cosines ${}_{F2},{}_{F2},$ and ${}_{F2}$ of force $F_2.$

$($d$)[$Points $0\mathrm{.}2/3]$ Compute the magnitude and direction of the resulting force $)=(F_{Rx}i+F_{Ry}j+F_{Rz}k$ out of the three forces $F_1,F_2,$ and $F_3.$