Learning Goal:

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

As shown, a $3\mathrm{.}1-$ lb ball is suspended at point $D$ inside a box with dimensions $w=9\mathrm{.}50ft,d=6\mathrm{.}80ft,$ and $h=4\mathrm{.}40ft.$ 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 $(-4\mathrm{.}40,-3\mathrm{.}70,2\mathrm{.}70)ft,$ point $B$ is located at $(2\mathrm{.}40,-3\mathrm{.}70,1\mathrm{.}90)ft,$ and point C is located at $(2\mathrm{.}40,5\mathrm{.}80,-1\mathrm{.}70)ft.$

Part A $-$ Determining Cartesian components of force

The tension in cable $DA$ has a magnitude of $T_{DA}=8\mathrm{.}91lb.$ Find the Cartesian components of tension $T_{DA},$ which is directed from $D$ to A$.$

Part B $-$ Determining an unknown force

If the tensions in cables $DA$ and $DB$ are $T_{DA}=8\mathrm{.}91lb$ and $T_{DB}=4\mathrm{.}91lb,$ respectively, what is the tension in cable DC$?$