$4.)$ Consider the $3$D space$-$truss shown below supported by ball$-$and$-$socket joints at A$,$B$,$D$.$ Force vector $F=-219i+361j+130k$

a$)$ Write down all the possible reaction forces at $A,B,D.$

$(6$ pts$)$

b$)$ Write down a vector $(1,j,k)$ equation for equilibrium based on forces

$(3$ pts$)$

c$)$ Write down a vector equation $(1,j,k)$ for equilibrium based on moments about any point of your choosing.

$(3$ pts$)$

d$)$ Solve for the values of all external reaction forces

$(6$ pts$)$

e$)$ Solve for forces in the $6$ members and indicate whether they are in tension or compression.

$(12$ pts$)$

$30$ POINTS