Problem $3$: $(35$ points$)$ Cable $CA$ extends from point $C($on the wall$)$ to point $A($off the wall$),$ as

shown in Figure $3.$ The scalar magnitude $T_{CA}$ of the vector tensile force $T_{CA}$ in cable $CA$ is equal

to $500$ N $.$ An $x-y-z$ coordinate system is drawn on the figure.

a$)$ Express the vector force $T_{CA}$ in terms of the unit vectors $i,j,$ and $k.$

b$)$ Find the moment $M_B$ of force $T_{CA}$ about point $B.$ Express the result in terms of the unit

vectors $i,j,$ and $k.$

c$)$ Find the unit vector $u_{DB}($directed from point $D$ to point $B)$ in terms of the unit vectors $i,j,$

and $k.$

d$)$ Find the scalar moment $M_{DB}$ of the force $T_{CA}$ about the line $DB($from point $D$ to point $B,$

not drawn on the figure$).$ Find the vector moment $M_{DB}$ of the force $T_{CA}$ about the line $DB$ in

terms of the unit vectors $i,j,$ and $k.$

e$)$ Find the scalar component $T_{DB}$ of the force $T_{CA}$ in the direction of line $DB($from point $D$ to

point $B).$ Find the angle $$ between the force $T_{CA}$ and line $DB.$ SHOW ALL STEPS