II$.$ Problems

$3.$ A rod $CD$ is attached to a wall at $D.$ There are two cables attached at end of the rod and at the wall. The tension in each cable acting at $C$ at end of the rod is known:

$\frac{?}{\text{b}\text{a}\text{r}}(T{)}_{CA}=(-7\mathrm{.}2$hat$()+8\mathrm{.}6$hat$()+2\mathrm{.}1$widehat$(k))kN,$ and$\frac{}{b}$

$ar(T{)}_{CB}=(-7\mathrm{.}4$hat$()+9\mathrm{.}3$hat$()-5\mathrm{.}0$widehat$(k))kN.$

a$.(5$ points$)$ Find the angle $$ between the two cables.

b$.(5$ points$)$ Find the projection of $\frac{?}{\text{b}\text{a}\text{r}}(T{)}_{CA}$ on the $CB$ cable.

$\frac{?}{\text{b}\text{a}\text{r}}(T)CA=(-7\mathrm{.}2i+8\mathrm{.}6J+2\mathrm{.}1k)kn\frac{?}{b}$

$ar(T{)}_{CB}=(7\mathrm{.}4i+9\mathrm{.}3J-5\mathrm{.}0k)kN\frac{,}{b}ar(T{)}_{(1)}.$

$,(-7\mathrm{.}2-7\mathrm{.}4)i+(8\mathrm{.}6+9\mathrm{.}3)J+(2\mathrm{.}1-5)k$

Tur.

$=$

$(T_{C{A}_{||}}{)}_{CB}=$