Problem # $3$: Rope DEC is connected to the rectangular lid ABCD at $D$ and $C$ and passes over a smooth hook at $E.(50$

points$)$

vec$(r{)}_{EC}=(40-10)hat()+(5-20)hat()+(15-0)hat(k)$

$=30$hat$()-15$hat$()+15$hat$(k)$

vec$(r{)}_{DE}=(10-0)hat()+(20-5)hat()+(0-15)hat(k)$

$=10$hat$()+15$hat$()-15$hat$(k)$

$0,0$ in

hat$({)}_{DE}=\frac{10}{18\mathrm{.}0277}$hat$()+\frac{15}{1810277}$hat$()-\frac{15}{18,0277}$hat$(k)$

$=$

hat$({)}_{DE}=$

a$.$ On the figure, denote the coordinates of $A,C,D$ and $E,$ and draw $r_{\frac{D}{E}}$ and $r_{EC}(10$ points$)$

b$.$ Use the space to the right of the figure to calculate the angle $$ between $ED$ and $EC,$ and the unit hat$({)}_{DE}$

$(20$ points$)$