earning Goal: o understand how to quantitatively determine whether a particle in a state of mechanical equilibrium.

$1$ statics, we make extensive use of Newton's first law, which tates that a particle, initially at rest, or moving in a straight line ith constant velocity, will remain in its current state unless the article is subjected to an unbalanced force system. If the sum of ne forces acting on a particle is zero, then it is in mechanical quilibrium. Although a particle is most likely at rest when in quilibrium, it could alternatively be in a state of constant motion. gure $$

$2$ of $2$Graphically, we can determine whether the sum of the iorces is so$,$ the sum of the forces acting on the particle is zero, ${\displaystyle \underset{?}{\overset{?}{}}}F=0.$ Although graphing force vectors in two dimensions is simple, graphing them in three dimensions is more difficult. Mathematically, we can express the forces as Cartesian vectors; for equilibrium, the sum of the forces' components in each direction is zero. Mathematically, this means that ${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0,{\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0,$ and ${\displaystyle \underset{?}{\overset{?}{}}}{F}_z=0.$

Part B

As shown, three forces, $F_1,F_2,$ and $F_3,$ act at the same point on an object. $($Figure $2)$ The point of application is the origin of a Cartesian coordinate syster $F_1,$ which has a magnitude of $F_1=14\mathrm{.}0kN,$ is in the $y-z$ plane and is described by an angle ${}_1=31\mathrm{.}0$ degrees. $F_2$ is in the $x-z$ plane and is described b integer lengths of a similar right triangle; its magnitude is $F_2=16\mathrm{.}5kN.$ If the sum of the forces is equal to zero, what is the magnitude of $F_3?$

Express your answer numerically in kilonewtons to three significant figures.

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