A three$-$legged structure is shown below. It is attached to the ground at points $,0$ and $C=(-3\mathrm{.}48,0,0)$ and connected to the ceiling at point $A=(-4\mathrm{.}42,3\mathrm{.}01,4\mathrm{.}34)$ The three legs connect at point $D=(0,2\mathrm{.}07,2\mathrm{.}00),$ where two forces, $F$ and $P,$ act. Force $F$ is given by $F=10\mathrm{.}0i-16\mathrm{.}0j+30\mathrm{.}0kN$;$P$ has magnitude $50\mathrm{.}0$ N and direction angles $=117\mathrm{.}0,=52\mathrm{.}5,$ and $=49\mathrm{.}4$ for the $x,y,$ and $z$ axes, respectively.$($ Figure $1)$

Part C $-$ Determining the force along a member

Determine the magnitude, $F_{DA},$ acting along member $DA,$ due to the applied force $F=10\mathrm{.}0i-16\mathrm{.}0j+30\mathrm{.}0kN$ Express your answer to three significant figures and include the appropriate units.

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$F_{DA}=$

$q,$

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Part D $-$ Finding the component of a force perpendicular to a direction

Given $F=10\mathrm{.}0i-16\mathrm{.}0j+30\mathrm{.}0kN,$ find the component of $F$ that acts perpendicular to member $DA$ such that the vector addition of the perpendicular and parallel components of $F(F=F+F_1)$ with respect to $D{A}^{\text{'}}$ equals $F.$ Express your answer in component form.

Express your answers, separated by commas, to three significant figures.

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