$,$Consider the force in $($Figure $1).$

Figure$1$ of $1$

A tetrahedron $\text{'}$A$\text{'}$ B C D is shown in the x y z space. Point $\text{'}$A$\text{'}$ is at the origin. Point D has all three coordinates positive and lies at $15$ feet above the x y plane, $10$ feet from the x z plane, and $5$ feet from the y z plane. Point C lies in the first quadrant of the x y plane. Point C is $6$ feet farther from the x z plane than point D and $8$ feet farther from the y z plane than point D$.$ Point B lies on the positive y axis, and it is $4$ feet farther from the x z plane than point C$.$ A force F is applied to the tetrahedron at point D and points toward point B$.$

Part A

If the moment of the force F

about the edge CA

of the tetrahedron has a magnitude of M

$=140$ lb$$ft

and is directed from C

toward A

$,$ determine the magnitude of F

$.$

Express your answer in pounds to three significant figures.

Activate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

F

$=$