Part A $-$ Determining Cartesian components of force

Learning Goal:

To determine Cartesian force components from magnitude and determine position and resultant vectors by summing Cartesian components.

As shown, a $2\mathrm{.}9-lb$ ball is suspended at point $D$ inside a box with dimensions $w=9\mathrm{.}50f{t}_{,}d=6\mathrm{.}60ft,$ and $h=4\mathrm{.}30ft.$ The ball is held in place by three cables anchored at points $A,B,$ and $C$ on the surface of the box.

point $D$ is the origin of the Cartesian coordinate system, point $A$ is located at $(-4\mathrm{.}40,-3\mathrm{.}80,2\mathrm{.}70)ft,$ point $B$ is located at $(2\mathrm{.}20,-3\mathrm{.}80,1\mathrm{.}70)ft,$ and point $C$ is located at $(2\mathrm{.}20,5\mathrm{.}70,-1\mathrm{.}60)ft.$

The tension in cable $DA$ has a magnitude of $T_{DA}=8\mathrm{.}69lb.$ Find the Cartesian components of tension $T_{DA},$ which is directed from $D$ to $A.$

Express your answers, separated by commas, to three significant figures.

View Available Hint$($s$)$

$T_{DA}=$

Part B $-$ Determining an unknown force

If the tensions in cables $DA$ and $DB$ are $T_{DA}=8\mathrm{.}69lb$ and $T_{DB}=5\mathrm{.}10lb,$ respectively, what is the tension in cable $DC?$

Express your answer to three significant figures and include the appropriate units.

View Available Hint$($s$)$

$T_{DC}=$