(Solved): Learning Goal: To determine Cartesian force components from magnitude and determine position and re ...

Learning Goal: To determine Cartesian force components from magnitude and determine position and resultant vectors by summing Cartesian components. As shown, a $2.7?\mathrm{lb}$ ball is suspended at point $D$ inside a box with dimensions $w=9.30\mathrm{ft},d=6.60\mathrm{ft}$, and $h=4.40\mathrm{ft}$. The ball is held in place by three cables anchored at points $A,B$, and $C$ on the surface of the box. If point $D$ is the origin of the Cartesian coordinate system, point $A$ is located at $(?4.40,?3.60,2.80)\mathrm{ft}$, point $B$ is located at $(2.20,?3.60,1.90)\mathrm{ft}$, and point $C$ is located at $(2.20,5.70,?1.60)\mathrm{ft}$. Part A - Determining Cartesian components of force The tension in cable $DA$ has a magnitude of $T_{DA}=6.75\mathrm{lb}$. 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. Part B - Determining an unknown force If the tensions in cables $DA$ and $DB$ are $T_{DA}=6.75\mathrm{lb}$ and $T_{DB}=4.13\mathrm{lb}$, respectively, what is the tension in cable $DC$ ? Express your answer to three significant figures and include the appropriate units.