As shown, a $2\mathrm{.}3-$lb

ball is suspended at point D inside a box with dimensions w$=9\mathrm{.}30$ ft

$,$ d$=6\mathrm{.}70$ ft

$,$ and h$=4\mathrm{.}50$ ft

$.$ The ball is held in place by three cables anchored at points A$,$ B$,$ and C on the surface of the box.The figure shows a rectangular box with the origin of the x y z axes positioned inside it$.$ The box has length d along the x axis, width w along the y axis, and height h along the z axis. A ball is positioned at the origin, at point D$.$ Point A is at the top vertex of the box, which has negative x and y coordinates. Point B is on the vertical edge of the box, which has positive x and negative y coordinates. Point C is at the bottom vertex of the box, which has positive x and y coordinates. Cables connect all these points to the ball.If point D is the origin of the Cartesian coordinate system, point A is located at $(4\mathrm{.}70,3\mathrm{.}50,2\mathrm{.}70)$ ft

$,$ point B is located at $(2\mathrm{.}00,3\mathrm{.}50,1\mathrm{.}70)$ ft

$,$ and point C is located at $(2\mathrm{.}00,5\mathrm{.}80,1\mathrm{.}80)$ ft

$.$ Part A $-$ Determining Cartesian components of force

The tension in cable DA has a magnitude of TDA$=6\mathrm{.}50$ lb

$.$ Find the Cartesian components of tension TDA

$,$ 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 TDA$=6\mathrm{.}50$ lb

and TDB$=4\mathrm{.}80$ lb

$,$ respectively, what is the tension in cable DC$?$

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

To determine Cartesian force components from magnitude and determine position

and resultant vectors by summing Cartesian components.

As shown, a $2\mathrm{.}3-$lb ball is suspended at point $D$ inside a box with dimensions

$w=9\mathrm{.}30ft,d=6\mathrm{.}70ft,$ and $h=4\mathrm{.}50ft.$ 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 $(-4\mathrm{.}70,-3\mathrm{.}50,2\mathrm{.}70)ft,$ point $B$

is located at $(2\mathrm{.}00,-3\mathrm{.}50,1\mathrm{.}70)ft,$ and point $C$ is located at

$(2\mathrm{.}00,5\mathrm{.}80,-1\mathrm{.}80)ft$

Part A $-$ Determining Cartesian components of force

The tension in cable $DA$ has a magnitude of $T_{DA}=6\mathrm{.}50lb.$ 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$)$

Part B $-$ Determining an unknown force

If the tensions in cables $DA$ and $DB$ are $T_{DA}=6\mathrm{.}50lb$ and $T_{DB}=4\mathrm{.}80lb,$ respectively, what is the tension in cable $DC?$

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

View Available Hint$($s$)$

$T_{DC}=$